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% Beginning of conm-m-l.let-e
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Following this letter are four files (CONM-M-L.STY, CONM-M-L.TEX,
CONM-M-CH1.TEX and CONM-M-L.CHECKLIST) to be used when preparing a paper in
AMS-LaTeX, for a volume in the Contemporary Mathematics series.  To make it
easier to load these files separately on your system, they are separated by
file delimiters.

The .STY file is based on AMSBOOK.STY. Instructions for using this file are
listed at the top.

The .TEX files together form a sample of the macros defined in the .STY file. 
Before preparing your paper, you should TeX CONM-M-L.TEX (CONM-M-CH1.TEX is input by
CONM-M-L.TEX) and print it to test the macros and to get instructions for their
use.

The .CHECKLIST file should be printed and used to help you avoid the most
common problems.

Once your paper has been accepted for publication in CONM-M, please send the
.TEX file to our Internet address: PUB-SUBMIT@MATH.AMS.COM.  When you send the
file please be sure to include a message that identifies the publication
series.

Should you have any technical questions, please contact our Technical Support
Group at 800-321-4AMS or 401-455-4080.  They can also be reached through
electronic mail at Internet: tech-support@math.ams.com.

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%-----------------------------------------------------------------------------
% Beginning of conm-m-l.sty
%-----------------------------------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This file is designed to work with AMSLaTeX version 1.1. It uses
% amsbook.sty as a base and modifies page size, top matter, section
% headings, etc. to produce CONM-M style.
%
% Instructions:
%
%  1. Create a file named  conm-m-l.sty ("-L" for LaTeX)
%     containing the lines from 
%      
%             %%% conm-m-l.sty 
%
%     through 
%
%             \endinput
%
%     Install the file in the same directory as amsart.sty.
%
%  2. In a document file, use \documentstyle{conm-m-l}.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% conm-m-l.sty
\input amsbook.sty
%
\textheight=49pc  \textwidth=29pc
\headsep=14pt
%
%      In AMS production, \parskip has no stretch component.
\parskip=0pt
%
%      \Large is not defined in amsart[10].sty in order to
%      conserve font memory. But we need it here for fourteen-point
%      titles.
\def\Large{\@setsize\Large{18\p@}\xivpt\@xivpt}
%
%      Change the baselineskip from 12pt to 13pt.
\def\@normalsize{\@setsize\normalsize{13\p@}\xpt\@xpt
  \abovedisplayskip 6\p@ \@plus 6\p@
  \belowdisplayskip \abovedisplayskip
  \abovedisplayshortskip \z@ \@plus 6\p@
  \belowdisplayshortskip 3\p@ \@plus 6\p@
  \let\@listi\@listI}
%
\normalsize
%
%      \footnotesize is changed only in order to change \@listi.
%
\def\footnotesize{\@setsize\footnotesize{10\p@}\viiipt\@viiipt%
  \abovedisplayskip 5\p@ \@plus 2.5\p@ minus2.5\p@%
  \belowdisplayskip \abovedisplayskip
  \abovedisplayshortskip \z@ \@plus 2\p@%
  \belowdisplayshortskip 4\p@ \@plus 2\p@ minus2\p@%
  \def\@listi{\topsep \z@ \parsep \z@ \itemsep \z@}}
%
%
%      CHAPTER TITLES
%
%      Change the numbering from roman numerals to numbers
\def\thechapter{\@arabic\c@chapter}
%
\def\@chapter[#1]#2{\refstepcounter{\@string\chapter}%
  \typeout{\chaptername\space\thechapter}%
  \def\\{\unskip\protect\space\ignorespaces}%
  \addcontentsline{toc}{\@string\chapter}{%
    \ifnum \c@secnumdepth >\m@ne
      \protect\numberline{\chaptername\ \thechapter.}\fi #2}%
  \chaptermark{\ifnum\c@secnumdepth >\m@ne \thechapter. \fi
       \ignorespaces#1\unskip}%
  \addtocontents{lof}{\protect\addvspace{10\p@}}%
  \addtocontents{lot}{\protect\addvspace{10\p@}}%
  \@makechapterhead{#2}\@afterheading}
%
\def\@makechapterhead#1{\begingroup \topskip 9pc\relax
  \defaultfont\bf\Large \centering
    \ifnum\c@secnumdepth>\m@ne
      \leavevmode \hskip-\leftskip
      \rlap{\vbox to\z@{\vss
          \centerline{\mediumseries\@normalsize
              \uppercase\expandafter{\chaptername}\enspace\thechapter}
          \vskip 34pt}}\hskip\leftskip\fi
     #1\par \endgroup
  \skip@55\p@ \advance\skip@-\normalbaselineskip
  \vskip\skip@ }
%
\def\@makeschapterhead#1{\begingroup \topskip 9pc\relax
  \defaultfont\bf\Large \centering
  #1\par \endgroup
  \ifx#1\contentsname\skip@36\p@
	\else
	\ifx#1\bibname\skip@36\p@
	 \else
 		 \skip@55\p@ 
	\fi
  \fi
\advance\skip@-\normalbaselineskip
  \vskip\skip@ }
%
%      SECTIONING COMMANDS
%
%      \@sect is changed in order to change the amount of space after
%      section numbers.
\def\@sect#1#2#3#4#5#6[#7]#8{%
\ifnum #2>\c@secnumdepth
  \let\@svsec\@empty
\else
  \refstepcounter{#1}%
  \edef\@svsec{\ifnum#2<\@m
             \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
%      Change the space after the period from \enspace to word
%      space.  Using \kern\fontdimen2\font makes the space
%      nonstretchable.
  \noexpand\rom{\csname the#1\endcsname.}\kern\fontdimen2\font}\fi
\@tempskipa #5\relax
\ifdim \@tempskipa>\z@ % then this is not a run-in section heading
  \begingroup #6\relax
  \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
  \endgroup
%      Remove unnecessary if@article test
  \csname #1mark\endcsname{%
    \ifnum #2>\c@secnumdepth\else \csname the#1\endcsname. \fi#7}%
  \ifnum#2>\@m
  \else \addcontentsline{toc}{#1}%
       {\ifnum#2>\c@secnumdepth
        \else \protect\numberline{%
                \ifnum#2<\@m
                 \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
               \csname the#1\endcsname.}\fi
           #8}%
  \fi
\else
  \def\@svsechd{#6\hskip #3\@svsec
    \@ifnotempty{#8}{\ignorespaces#8\unskip
      \ifnum\spacefactor<1001.\fi}%
      \ifnum#2>\@m
      \else
        \addcontentsline{toc}{#1}%
            {\ifnum#2>\c@secnumdepth
             \else \protect\numberline{%
               \ifnum#2<\@m
               \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
               \csname the#1\endcsname.}\fi
             #8}\fi}%
\fi
\@xsect{#5}}
%
\numberwithin{section}{chapter}
\def\section{\@startsection{section}% counter name
{1}% sectioning level
{\z@}% indent to the left of the section title
{12\p@\@plus3\p@}% vertical space above
{5\p@}% vertical space below
{\centering\bf}}% font of title
%
\def\subsection{\@startsection{subsection}% counter name
{2}% sectioning level
{\parindent}% indent to the left of the subsection title
{6\p@\@plus2\p@}% vertical space above
{-.5em}% following text is run in, after a horizontal space of this amount.
% The minus sign is to get horizontal space instead of vertical space.
{\bf}}% The font of the subsection title
%
\def\subsubsection{\@startsection {subsubsection}% counter number
{3}% sectioning level
{\parindent}% %% indent to the left of the subsubsection title
{6\p@\@plus2\p@}%  vertical space above
{-.5em}% horizontal space after (negative sign will be canceled)
{\it}}% font of subsubsection title
%
% Levels below C-head (\subsubsection) are undefined in AMS
% production documentstyles.
%
\def\paragraph{\@latexerr{\noexpand\paragraph not defined
  in this \string\documentstyle}\@eha}
\def\subparagraph{\@latexerr{\noexpand\subparagraph not defined
  in this \string\documentstyle}\@eha}
%
%      Set a wider width for page numbers in a table of contents:
\def\@pnumwidth{3em}
%
%      Don't use anything lower than \section level in table
%      of contents:
\setcounter{tocdepth}{1}
%
\newbox\TestChapwd

\def\@tocline#1#2#3#4#5#6{\par
\setbox\TestChapwd=\hbox{Chapter\ \thechapter.\hskip1em}%
  \addpenalty\@secpenalty\addvspace{#1}%
  \begingroup
	\ifx#1\bigskipamount%chapter
	\@tempdima\wd\TestChapwd\else
		\@tempdima#2\fi\relax % used by \numberline
  \parindent\z@ \leftskip#4 \rightskip\@pnumwidth \parfillskip-\@pnumwidth
  {#3\leavevmode #5
	\hfil \hbox to\@pnumwidth{\hss #6}}\hangindent\@tempdima\par\nobreak
  \endgroup}
%
\def\l@chapter{\@tocline\bigskipamount{2em}{\normalshape}{0pt}}
\def\l@section{\@tocline{0pt}{2em}{\normalshape}{1pc}}
%
%      Set \topsep to 0 in \@listI.
\def\@listI{\leftmargin\leftmargini
  \parsep\z@skip \topsep\z@skip \itemsep\z@skip}
\let\@listi\@listI
\@listi
%
%      Cites in AMS proceedings volumes are typically typeset
%      in bold rather than roman.
\def\@cite#1#2{\rom{\mediumseries[{\bf#1}\if@tempswa , #2\fi]}}
%
%      No extra space around definition-style enunciations.
\def\th@definition{\theorempreskipamount\z@
    \theorempostskipamount\theorempreskipamount
    \normalshape}
\def\th@remark{\theorempreskipamount6\p@\@plus6\p@
    \theorempostskipamount\z@\@plus6\p@
    \def\theorem@headerfont{\it}\normalshape}
%
%      Use small caps instead of italic for \proofname, and paragraph
%      indent instead of noindent.
\def\pf{%
  \par\topsep6\p@\@plus6\p@
  \trivlist \itemindent\normalparindent
  \item[\hskip\labelsep\sc\proofname.]\ignorespaces}
%
%      Change the running head font from \small to \footnotesize 
\def\ps@headings{\let\@mkboth\markboth
  \let\@oddfoot\@empty\let\@evenfoot\@empty
  \def\@evenhead{\footnotesize \rlap{\thepage}\hfil
    \expandafter\expandafter\expandafter\expandafter\expandafter
    \expandafter\expandafter\uppercasetext@
    \expandafter\expandafter\expandafter\expandafter\expandafter
    \expandafter\expandafter{\leftmark}%
    \hfil}%
  \def\@oddhead{\footnotesize\hfil
    \expandafter\expandafter\expandafter\expandafter\expandafter
    \expandafter\expandafter\uppercasetext@
    \expandafter\expandafter\expandafter\expandafter\expandafter
    \expandafter\expandafter{\rightmark}%
    \hfil \llap{\thepage}}%
  \def\chaptermark##1{\@mkboth{##1}{##1}}%
  \let\sectionmark\markright}

\def\ps@myheadings{\let\@mkboth\@gobbletwo
  \def\@oddhead{\footnotesize\rightmark \hfil\thepage}\let\@oddfoot\@empty
  \def\@evenhead{\footnotesize\thepage\hfil\leftmark}\let\@evenfoot\@empty
  \let\chaptermark\@gobble \let\sectionmark\@gobble}
%
%       Some computations to make the \textheight come out
%       to an even multiple of baselineskip (after taking
%       \topskip etc. into account).
\advance\textheight by -\headheight
\advance\textheight by -\headsep
\advance\textheight by -\normalbaselineskip
\advance\textheight by \topskip
%
%      We now have the right value for \textheight except that we need
%      to round it. If \baselinestretch is changed in an actual
%      document, this \textheight will most likely be off and you'll get
%      underfull vbox messages.
\advance\textheight by.5\normalbaselineskip
\divide\textheight by\normalbaselineskip
\multiply\textheight by\normalbaselineskip
%
\advance\topmargin by -.25 true in
%
%      LIST ENVIRONMENTS
%
%      Change first-level `enumerate' numbering style from arabic
%      to roman numeral.
\renewcommand{\labelenumi}{(\roman{enumi})}
%
%      Change \enumerate and \itemize to increase \partopsep.
\def\enumerate{\ifnum \@enumdepth >3 \@toodeep\else
      \advance\@enumdepth \@ne
      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
      {\csname label\@enumctr\endcsname}{\usecounter
        {\@enumctr}\partopsep6\p@\def\makelabel##1{\hss\llap{\normalshape##1}}}\fi}
%
\def\itemize{\ifnum\@itemdepth>3 \@toodeep
  \else \advance\@itemdepth\@ne
  \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
  \list{\csname\@itemitem\endcsname}%
  {\partopsep6\p@\def\makelabel##1{\hss\llap{\normalshape##1}}}\fi}
%
%      Change \bibname from the default in amsbook.sty of "Bibliography"
\def\bibname{References}
%
%      Change font size to \normalsize, and change
%      the form of the list counter (see amslatex.bug, 2-JUL-1991)
\def\thebibliography#1{\chapter*\bibname
  \defaultfont\normalsize\labelsep .5em\relax
  \list{\@arabic\c@enumi.}{\settowidth\labelwidth{#1.}\leftmargin\labelwidth
  \advance\leftmargin\labelsep \usecounter{enumi}}\sloppy
  \clubpenalty9999 \widowpenalty\clubpenalty  \sfcode`\.\@m}
%      TOPMATTER 
%
\def\copyrightyear{0000}
\def\copyrightyearmodC{00}
\def\ISSN{0000-0000}
\def\copyrightprice{\$1.00\;+\;\$.25 per page}
\def\currentvolume{00}
\def\currentyear{0000}
%
\def\@maketitle{\cleardoublepage \thispagestyle{empty}%
\begingroup \topskip\z@skip
\null\vfil
\begingroup
        \centering \large\bf \openup\medskipamount
        \expandafter\uppercasetext@\expandafter{\@title}\vfil
        \def\and{\par\bigskip}\mediumseries\@authors\vfil
\endgroup
\vfil\vfil
\newpage
\ifx\@empty\@subjclass \else
1991 {\it Mathematics Subject Classification}.\enspace
\@subjclass.\vfil
\fi
\vfil
\begingroup
        \parskip\medskipamount
        \ifx\@empty\@translator \else
        Translator: \@translator \@@par\fi
        \@thanks\@@par
\endgroup
\vfil
\ifx\@empty\@keywords \else
{\it Key words and phrases.}\enspace \@keywords.\vfil
\fi
\expandafter\@ifnotempty\expandafter{\the\@addresstoks}{%
Author addresses:\par
\@setaddress\vfil}%
\vfil\vfil
\endgroup}
%
\pagenumbering{arabic}
\onecolumn
\mark{{}{}}
\ps@headings

\endinput
%-----------------------------------------------------------------------------
% End of conm-m-l.sty
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%-----------------------------------------------------------------------------
% Beginning of conm-m-l.tex
%-----------------------------------------------------------------------------
%
% This is a sample file for use with AMS-LaTeX. It provides an example of
% how to set up a file to be typeset with AMS-LaTeX.
%
% This is the driver file.  Separate chapters should be included at the end
% of this file. (see how conm-m-ch1.tex was included.)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentstyle{conm-m-l}
\newtheorem{lemma}{Lemma}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{definition}{Definition}[section]

\theoremstyle{definition}
\newtheorem{example}{Example}[section]

\numberwithin{equation}{section}

%      \cprime is used in Russian names for `soft sign'. The
%      references section uses this.
\newcommand{\cprime}{$'\mathsurround=0pt$}

\begin{document}
\pagenumbering{roman}
\title{Sample \AmS-\LaTeX{} Electronic Manuscript for 
Contemporary Mathematics}

\address{Department of Mathematics, Northeastern University, Boston,
Massachusetts 02115} % Research address for author one
\curraddr{Department of Mathematics and Statistics,
Case Western Reserve University, Cleveland, Ohio 43403}
\email{XYZ@@Math.AMS.com}
\address{Mathematical Research Section, School of Mathematical Sciences,
Australian National University, Canberra ACT 2601, Australia} %address for 
%                                                             author two

\date{July 2, 1991}
\subjclass{Primary 54C40, 14E20; Secondary 46E25, 20C20}

%  \thanks will become a 1st page footnote.
\thanks{The first author was supported in part by NSF
Grant \#000000.}

\maketitle

\begin{abstract}
This paper is a sample prepared to illustrate for authors
the use of the \AmS-\LaTeX{} Version~1.1 package and the CONM-M documentstyle.

The file used to prepare this sample is {\bf CONM-M-L.tex}; an author
should use the coding in that file as a model.
\end{abstract}

\tableofcontents

\pagenumbering{arabic}
\input{conm-m-ch1}
\end{document}

%-----------------------------------------------------------------------------
% End of conm-m-l.tex
%-----------------------------------------------------------------------------
%------------------------------------------------------------------------------
% Beginning of conm-m-l.checklist
%------------------------------------------------------------------------------
		     Check List for Electronic Manuscripts

				  CONM-M Volumes


- The author should proofread the paper before submitting to the AMS.

- In chapter titles, capitalize the first and last words and all nouns,
  pronouns, adjectives, adverbs, and verbs; lowercase articles, conjunctions,
  and prepositions unless they are first or last word.

- The running heads for the left-hand (even-numbered pages) should have the
  chapter title all in uppercase.  Shorten the title in the running heads only 
  if it is necessary to make it fit on one line.

- The running heads for the right-hand (odd-numbered pages) should have
  the main heading title (shortened if necessary) all in uppercase.

- Citations in the manuscript should be coded using "\cite".

- References should include all available information.

- The .tex files should include NO "input" files.

- All definitions should be  at the top of the file and none of them should
  redefine any LaTeX commands.

- Definitions should be used consistently throughout the paper.

- No definitions should be used for formatting text; only the LaTeX 
  environments should be used.

- The file should contain no line and/or page breaks.

- A covering letter should be included with the electronic submission.  The 
  letter should clearly identify the author, title and intended publication
  series.  It should also tell us where the author can be reached throughout
  the publication process.  

%------------------------------------------------------------------------------
% End of conm-m-l.checklist
%------------------------------------------------------------------------------
%-----------------------------------------------------------------------------
% Beginning of conm-m-ch1.tex
%-----------------------------------------------------------------------------
%
% This is a sample file for use with AMS-LaTeX. It provides an example of
% how to set up a file to be typeset with AMS-LaTeX.
%
% This is the data file.  It is input by conm-m-l.tex.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\chapter[Maximal Ideals in Subalgebras of $C(X)$]{Sample Paper for CONM-M,\\
On Maximal Ideals in Subalgebras of $C(X)$}

\section{Introduction}

This sample paper illustrates the use of the AMSBOOK style file of
\AmS-\LaTeX{} Version~1.1 with additional macros for the series  {\it
YYY}. In this sample paper, brief instructions to authors will be
interspersed with mathematical text extracted from (purposely
unidentified) published papers.  For instructions on preparing
mathematical text, the author is referred to {\it The Joy of \TeX},
second edition, by Michael Spivak \cite{spivak:jot} and {\it \LaTeX{}: A
Document Preparation System} by Leslie Lamport \cite{lamport:latex}.

\subsection{Top matter}
The input format and content of the top matter can be best understood
by examining the first part of the sample file {\bf CONM-M-L.tex}, up
through the \verb+\begin{document}+ instruction.
If it is desired to have chapter numbers be uppercase Roman numerals rather
than Arabic numbers, you must type  
\verb+\renewcommand{\thechapter}{\Roman{chapter}}+ before
\verb+\chapter+ is called.

The chapter title and the current, main-level heading title appear in the
appropriate running heads automatically. If the full title or heading would
require more than one line to fit in the running head, an abbreviated form,
including the correct chapter or section number, should be substituted using 
the bracketed options allowed in \LaTeX\ for chapters and sections (see pages
157--158 in {\it \LaTeX{}: A Document Preparation System}).


\subsection{Fonts}
The fonts used in this paper are from the Computer Modern family; they
should be available to all authors preparing papers with these macros.
However, the final copy may be set by the AMS using other fonts.  

\subsection{A mathematical extract}
The mathematical content of this sample paper has been extracted from
published papers, with no effort made to retain any mathematical sense.
It is intended only to illustrate the recommended manner of input.

Mathematical symbols in text should always be input in math mode as
illustrated in the following paragraph.

A function is invertible in $C(X)$ if it is never zero, and in $C^*(X)$ if
it is bounded away from zero. In an arbitrary $A(X)$, of course, there
is no such description of invertibility which is independent of the 
structure of the algebra. Thus in \S 2 we associate to each noninvertible
$f\in A(X)$ a $z$-filter $\cal Z (f)$ that is a measure of where
$f$ is ``locally'' invertible in $A(X)$. This correspondence extends to
one between maximal ideals of $A(X)$ and $z$-ultrafilters on $X$.
In \S 3 we use the filters $\cal Z (f)$ to describe the intersection of 
the free maximal ideals in any algebra $A(X)$. Finally, our main result
allows us to introduce the notion of $A(X)$-compactness of which 
compactness and realcompactness are special cases. In \S 4 we show how
the Banach-Stone theorem extends to $A(X)$-compact spaces.

\section{Theorems, lemmas, and other proclamations}

Theorems and lemmas are varieties of \verb+theorem+ environments.  In this
document, a \verb+theorem+ environment called \verb+lemma+ has been created,
which is used below. Also, there is a  proof, which is in the predefined
\verb+pf+ environment.  The lemma and proof below illustrate the use of 
the \verb+enumerate+ environment. 

\begin{lemma}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
\item If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup F$-%
regular.

\item If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.

\end{enumerate}
\end{lemma}

\begin{pf}
\begin{enumerate}

\item  Obvious.

\item Let $h, k\in A(X)$ satisfy $hf|_E=1$ and $kf|_F=1$. Let
$w=h+k-fhk$. Then $fw|_{E\cup F}=1$.

\item Let $h=\max\{c,f\}$. Then $h|_E=f|_E$ and $h\ge c$. So $0<h^{-1}
\le c^{-1}$. Hence $h^{-1} \in C^*(X)\subseteq A(X)$, and 
$h^{-1} f|_E=1$.

\end{enumerate}
%      To place the \qedsymbol properly:
\qedsymbol\renewcommand{\qed}{}
\end{pf}

Another \verb+theorem+-type environment was defined at the beginning of this
document, called \verb+definition+. Here is an example of it:

\begin{definition}
For $f\in A(X)$, we define
\begin{equation}
\cal Z (f)=\{E\in Z[X]\: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{definition}

\section{Roman type}

Numbers, punctuation, (parentheses), [brackets], $\{$braces$\}$, and
symbols used as tags should always be set in roman type.  The following
sample theorem illustrates how to code for roman type within the
statement of a theorem.

\begin{theorem}
Let $\cal G$ be a free nilpotent-of-class-$2$ group of rank
$\ge 2$ with carrier $G$ and let
$$m : G\times G \to Z$$
satisfy \rom{(2.21)}, \rom{(2.22)}, and \rom{(2.24)}, and define
$\kappa$ by \rom{(2.23)}.  Then this kappa-group is kappa-nilpotent
of class $2$ and kappa-metabelian, that is to say, it satisfies
\rom{S2} and \rom{S3}, but it is kappa-abelian if, and only if,
\begin{equation}
m(x,y) = -1\quad\text{for all $x, y \notin G'$}.
\end{equation}
\rom{(}Thus \rom{(3.1)} implies the trivial consequence
\rom{(2.1)}.\rom{)}  Assume now that \rom{(3.1)} does not hold,
so that the kappa-group is kappa-nonabelian.  Assume further that $m$
is not constant outside $G'$ \rom{(}inside $G'$ the values of $m$
clearly do not matter\rom{)}.  Then $\kappa$ is neither left nor right
linear, that is to say, neither \rom{S4} nor \rom{S5} holds:
\rom{I1} again holds, but none of \rom{I2--I5}.  As before,
\rom{I6} is equivalent to \rom{(2.25)}.  Now \rom{I7$'$}, however,
is equivalent to a condition similar to \rom{(2.25)}, namely
\begin{equation}
m(xz\sigma, yz\sigma) = m(x,y)\,.
\end{equation}
\end{theorem}

Letters used as abbreviations rather than as variables or constants
are set in roman type.  Use the control sequences \cite[p.~95]{spivak:jot}
for common mathematical functions and operators like $\log$ and $\lim$,
For bibliographical references, use \verb+\cite+ as illustrated
in the previous sentence.

\section{References}

To produce a bibliography, use the environment named
\verb+thebibliography+. Input each reference as you would normally do in
\LaTeX{} \cite{lamport:latex}. Arrange the references in alphabetical
order by the last name of the first named author.  The references at the
end of this sample file have been chosen to illustrate the coding of the
most common types of references. Use the abbreviations of names of
journals as given in annual indexes of {\it Mathematical Reviews}.
The sample references have been labeled with numbers, using
\verb+\bibitem{...}+. To get letter labels use, for example,
\verb+\bibitem[C1]{...}+.

References are set with hanging indentation.  The widest label should be
entered as the argument of the {\tt thebibliography} environment, if you
are not using Bib\TeX{} (which automatically determines the widest
label). For example, a bibliography containing more than a hundred
references would require three-digit number labels:
\begin{centering}\smallskip
\begin{verbatim}
\begin{thebibliography}{000}
\end{verbatim}
\smallskip\end{centering}

\section{Figures}

Figures to be inserted later should be handled using \LaTeX's \verb+figure+
environment.  The amount of space left should equal the exact height of the
figure.  Extra space around the figure will be provided automatically.  The
positioning of figures may need to be changed to obtain the best possible page
layout.  Thus it is important to label your figures and use the labels in the
text when referring to figures.  The figure caption should be positioned below
the figure.

In most cases, figures will be rendered for consistency of style within a
book.  Please provide figure manuscript drawn in black ink with clean,
unbroken lines on nonabsorbent paper.

\begin{example}
For the link in Figure 1.1, the Massey product $\langle u_1, u_2, u_3,
u_4, u_5\rangle$ in $S^3-L$ is defined and consists of all
integer multiples of $\gamma_{1,5}$.  For the link in Figure 1.2,
the Massey product $\langle u_1, u_2, u_3, u_4, u_5\rangle$ in
$S^3-L$ contains the single element $\gamma_{1,5}$.  Since the links
in Figures 1.1 and 1.2 are homotopic, the example indicates that Massey
products in $S^3-L$ with distinct $u_j$'s do not, in general,
determine homotopy invariants of the link.  For the link in Figure 1.1
and the link in Figure 1.2, the Massey product $\langle u_1, u_2, \dots,
u_5\rangle$ in $\{S^3-L_i\}_{i=1}^5$ contains the single element
$\gamma_{1,5}$.
\end{example}

%  art work measures 11.5pc for figure 1, 7pc for figure 2

\begin{figure}[t]
\vskip 11.5pc
\caption{Only the word {\it figure} is set cap/small caps.  Any other words are
regular text.}
\end{figure}

\begin{figure}[t]
\vskip 7pc
\caption{}
\end{figure}


\section{Other headings}

\subsection{A subsection}  We conclude by noting that another characterization
of $A$-compactness follows from Mandelker. We call a family $\cal S$ of closed
sets in $X\ A$-stable if every $f\in A(X)$ is bounded on some member of $\cal
S$. Then one can show that a space is $A$-compact if and only if  every
$A$-stable family of closed sets with the finite intersection property has
nonempty intersection.

\subsubsection{A second-level subheading}

This paragraph is included only to illustrate the appearance of a
sub-subsection.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibliographystyle{amsplain}

\begin{thebibliography}{10}

\bibitem{arnold:sing}
 V. L. Arnol\cprime d, A. N. Varchenko, and S. M. Gusein-Zade,
 {\em Singularities of differentiable maps.} I,
  ``Nauka'', Moscow, 1982 (Russian);
English transl. Birkh\"auser, 1985.

\bibitem{arnold:sing2}
\bysame,
 {\em Singularities of differentiable maps.}~II,
  ``Nauka'', Moscow, 1984;
English transl., Birkh\"auser, 1988.


\bibitem{bass:jacobian}
H. Bass, E. H. Connell, and D. Wright,
{\em The Jacobian conjecture}, Bull. Amer. Math. Soc.
 {\bf 7} (1982), 287--330.

\bibitem{bass:flows}
H. Bass and G. H. Meisters,
{\em Polynomial flows in the plane}, Adv. in Math.
 {\bf 55} (1985), 173--203.

\bibitem{coomes:injectivity}
B. Coomes,
{\em Polynomial flows, symmetry groups, and conditions sufficient for 
        injectivity of maps},
 Ph.D. Thesis, Univ. Nebraska-Lincoln, 1988.


\bibitem{coomes:lorenz}
\bysame,
{\em The Lorenz system does not have a polynomial flow},
{J. Differential Equations} (to appear).

\bibitem{formanek:gener}
E. Formanek,
{\em Generating the ring of matrix invariants},
Lecture Notes in Math., vol. 1197,
Springer-Verlag, Berlin and New York,
1986, pp. 73--82.

\bibitem{meisters:poly}
\bysame,
{\em Polynomial flows on $\hbox{\bf R}^n$},
Proc. Semester on Dynamical Systems (Warsaw, Autumn 1986),
Springer-Verlag,
Berlin, Heidelberg, and New York
(to appear).

\bibitem{osher:shock}
S. Osher,
{\em Shock capturing algorithms for equations of mixed type},
 Numerical Methods for Partial Differential Equations
(S. I. Hariharan and T. H. Moulton, eds.),
  Longman, New York, 1986, pp. 305--322.

\bibitem{ostro:nonlin}
L. A. Ostrovsky,
{\em Nonlinear internal waves in a rotating ocean},
Part 2, Oceanology {\bf 18} (1978), 181--191.

\bibitem{petrov:ellip}
G. S. Petrov,
{\em Elliptic integrals and their nonoscillatory behavior},
Funktsional. Anal. i Pri\-lo\-zhen. {\bf 20} (1986), 46--49;
English transl. in Functional Anal. Appl. {\bf 20} (1986).

\bibitem{spivak:jot}
M. D. Spivak,
{\em The Joy of \TeX{}}, second edition, Amer. Math. Soc., Providence, R.~I., 
1990.

\bibitem{lamport:latex} Leslie Lamport, {\em \LaTeX{} -- A Document Preparation
System}, Addison-Wesley, Reading, Mass., 1986.

\end{thebibliography}

\endinput

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