%% @texfile{
%%     filename="amsl-art.tex",
%%     version="1.1a",
%%     date="30-JUL-1991",
%%     filetype="AMS-LaTeX: documentation",
%%     copyright="Copyright (C) American Mathematical Society,
%%            all rights reserved.  Copying of this file is
%%            authorized only if either:
%%            (1) you make absolutely no changes to your copy
%%                including name; OR
%%            (2) if you do make changes, you first rename it to some
%%                other name.",
%%     author="American Mathematical Society",
%%     address="American Mathematical Society,
%%            Technical Support Group,
%%            P. O. Box 6248,
%%            Providence, RI 02940,
%%            USA",
%%     telephone="401-455-4080 or (in the USA) 800-321-4AMS",
%%     email="Internet: Tech-Support@Math.AMS.com",
%%     codetable="ISO/ASCII",
%%     checksumtype="line count",
%%     checksum="496",
%%     keywords="amslatex, ams-latex, tex",
%%     abstract="This file contains input for a sample article
%%            illustrating the proper way to prepare such input
%%            for electronic submission to the AMS."
%%     }
%*********************************************************
%
% AMS-LaTeX 1.1 file for a sample article for electronic submission.
%
\documentstyle{amsart}
%
%  Macros that should be in AMS-LaTeX.
%  \LaTeX is already defined, but it does not work properly in sizes
%  other than ten point.
\makeatletter
\def\LaTeX{\leavevmode L\raise.42ex
    \hbox{\kern-.3em\size{\sf@size}{0pt}\selectfont A}\kern-.15em\TeX}
\makeatother
\newcommand{\AMSLaTeX}{\protect\AmS-\protect\LaTeX}
\newcommand{\BibTeX}{{\rm B\kern-.05em{\sc i\kern-.025emb}\kern-.08em\TeX}}

%  In this article, we prefer to have theorems and related structures
%  treated as subsections, to keep them distinct from the "real" sections;
%  section is the default level for theorem headings.

\newtheorem{thm}{Theorem}[subsection]
\newtheorem{lem}[thm]{Lemma}

\theoremstyle{definition}
\newtheorem{defn}{Definition}[subsection]
\newtheorem{exmp}{Example}[subsection]

%  In this article, we will have some figures labeled "a", "b", etc.
%  Provide a quick and dirty method of adding the letter to the label.
\newcommand{\subfig}{a}

%  In an example there are some cross-references to nonexistent equations.
%  Provide some dummy labels so that the input will look normal.
%  And adjust the form of the equation numbers to conform to the example.
\makeatletter
\def\@currentlabel{2.1}\label{e:dispaa}
\def\@currentlabel{2.21}\label{e:dispau}
\def\@currentlabel{2.22}\label{e:dispav}
\def\@currentlabel{2.23}\label{e:dispaw}
\def\@currentlabel{2.24}\label{e:dispax}
\def\theequation{\thesection.\@arabic\c@equation}
\makeatother

%  We will also have a list with alphabetic labels at the first level.
%  This definition can be used to avoid entering [optional] labels for
%  every item.
\makeatletter
\def\alphenumi{%
  \def\theenumi{\alph{enumi}}%
  \def\p@enumi{\theenumi}%
  \def\labelenumi{(\@alph\c@enumi)}}
\makeatother


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

\begin{document}

\title[Sample \AMSLaTeX{} Electronic Article]%
{Sample \AMSLaTeX{} Electronic Manuscript for a Journal or Proceedings
 Article,\\
 On Maximal Ideals in Subalgebras of $C(X)$}
\author{Author One}
\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}  %Current address for author one
\email{XYZ@@Math.AMS.com}
%  \thanks will become a 1st page footnote.
%  Don't type a period at the end; it will be supplied.
\thanks{The first author was supported in part by NSF
 Grant \#000000}
\author{Author Two}
\address{Mathematical Research Section, School of Mathematical Sciences,
 Australian National University, Canberra ACT 2601, Australia}
\email{ABC@@mathsci.anu.edu.au}
\thanks{The final version of this paper will be submitted for
 publication elsewhere}

\keywords{Author's key words go here}
%  Math Subject Classifications 
\subjclass{54C40, 14E20; Secondary 46E25, 20C20}

\maketitle

\begin{abstract}
This paper is a sample prepared to illustrate for authors the use of
the {\tt amsart} style of \AMSLaTeX{} Version~1.1.  An article of this
sort is suitable for publication in a journal or in a collection, such
as the proceedings of a conference.

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

\section{Introduction}

This sample paper illustrates the use of the \AMSLaTeX{} Version~1.1
{\tt amsart} style.
In this sample paper, brief instructions to authors are 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}, by Michael Spivak
\cite{Spi} and to the {\bf \AMSLaTeX{} User's Guide}.  Detailed
instructions for preparation of the structural elements of a paper are
given in the {\bf Guidelines for Preparing Electronic Manuscripts}, to
which this sample paper is one of several appendixes.


\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 amsl-art.tex}, up
to the first {\tt\char`\\section} instruction.

The top matter includes both elements that must be input by the author
and a few that are provided automatically.  For details, see the
the {\bf Top matter} section in above-mentioned {\bf Guidelines}.


\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 similar structures}
%
Theorems and lemmas and similar structures are all handled with
variations on the \verb|theorem| environment.  This is described in the
{\bf \AMSLaTeX{} User's Guide} [p.~32].

The lemma below uses the {\tt plain } theorem style and a heading at the
subsection level (section is the default, but a variation is used in
this sample article).

The lemma and proof illustrate the use of the \verb|enumerate|
environment to create lists.  The labels in these lists are not the
default ones (which would be (1), (2), etc.).  In the lemma, the
desired labels are entered using the optional \LaTeX{} bracket
notation; in the proof, the labels are generated automatically,
after invoking a command {\tt \char`\\alphenumi} that was defined
in the preamble of {\bf amsl-art.tex} for that purpose.

Also in the proof, note the special handling of the
{\tt \char`\\qed}, which would ordinarily be set on a line
by itself, after the end of the {\tt enumerate} environment.

\begin{lem}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
%  [want item labels of the form (a), (b), etc.]
\item[(a)] If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item[(b)] If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup F$-%
regular.
\end{enumerate}
\end{lem}

\begin{pf}
\begin{enumerate}
\alphenumi % Defined in the preamble.
\item Obvious.

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

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

\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{thm}
Let $\cal G$ be a free nilpotent-of-class-\rom{2} group of rank
$\ge 2$ with carrier $G$ and let
\begin{equation}
m : G\times G \to Z
\end{equation}
satisfy \rom{\eqref{e:dispau}}, \rom{\eqref{e:dispav}}, and
\rom{\eqref{e:dispax}}, and define $\kappa$ by
\rom{\eqref{e:dispaw}}.  Then this kappa-group is kappa-nilpotent
of class \rom{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 $x, y \notin G'$}.
\label{e:dispba}
\end{equation}
\rom{(}Thus \eqref{e:dispba} implies the trivial consequence
\rom{\eqref{e:dispaa}}.\rom{)}
\end{thm}

There are some other elements that should always be set in roman type.
Control sequences should be used for common mathematical functions and
operators like $\log$ and $\lim$ \cite[Chapter 14]{Spi}, and
\verb|\cite| should always be used when citing a reference.  Detailed
instructions are given in the {\bf Document body, roman type} section
in the above-mentioned {\bf Guidelines}.


\section{References}
%
Instructions for the input of references are given in the
{\bf Guidelines} mentioned above.

The sample references have been chosen to illustrate the coding of the
most common types of references.  These references have been labeled
with numbers, which were produced automatically by \BibTeX{} using the
style {\bf amsplain.bst}.  This style takes the number with the most
digits as the model from which the width of the left margin is established.
``Key''-type labels may also be used;
see the instructions in the {\bf Guidelines} and also the sample monograph
chapter that accompanies them, where that style has been used.

A bibliography prepared with \BibTeX{} always begins as a separate file.
The references for this paper were originally in the file {\bf amsl-art.bbl},
which can be recreated by running the file {\bf amsl-bib.bib} through
\BibTeX{} using the {\bf amsplain.bst} style.  Comments in the source file
for this article, {\bf amsl-art.tex}, give further details.


\section{Figures}
%
Figures are handled as inserts, with an amount of space indicated that
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 them.  The figure caption should be positioned below
the figure.

Additional instructions for figures and other inserts, including
instructions for preparing art work, are given in the {\bf Guidelines}.
Note that the figures in this example are denoted ``a'' and ``b''.
This requires that the figure counter be adjusted so that it holds
the same value for both; to see how this is done, check the coding
in the input file.

\begin{exmp}
For the link in Figure \ref{f:afig}, 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 \ref{f:bfig},
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 \ref{f:afig} and \ref{f:bfig} 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 \ref{f:afig} and the link in Figure \ref{f:bfig}, 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{exmp}

%  art work measures 14.5pc for figure a, 11pc for figure b

\begin{figure}[t]
  \makeatletter
  \makeatother
  \renewcommand{\thefigure}{\arabic{figure}\rom{\subfig}}
  \vspace{14.5pc}
  \caption{}  % figure a
  \label{f:afig}
  \vspace{11pc}
  \renewcommand{\subfig}{b}
  \addtocounter{figure}{-1}
  \caption{}  % figure b
  \label{f:bfig}
\end{figure}

\section{Other headings}
%
\subsection{A subheading}
We conclude by noting that another characterization of $A$-compactness
follows from Mandelker \cite{Mar}. 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 (as in \cite{Mar}) 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-subheading.

\subsubsection{Comment on the reference labels}
The references were prepared with \BibTeX{} using the style {\tt amsplain}.
This style automatically numbers the references, taking the number with
the most digits as the model from which the width of the left margin
is established.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  When BibTeX is used to create a bibliography, the LaTeX input file
%%  must include three commands of the following form.  When run through
%%  LaTeX, they will create the .aux file required by BibTeX to select
%%  the appropriate items from the specified .bib file and create a
%%  .bbl file.
%%
%\nocite{*}
%\bibliographystyle{amsplain}
%\bibliography{amsl-bib}
%%
%%  After the article is completed and the bibliography checked, to make
%%  sure that no changes need to be made in the original .bib file which
%%  require BibTeX to be rerun, the \nocite, \bibliographystyle and
%%  \bibliography commands should be commented out or removed, and the
%%  contents of the .bbl file inserted in their place, as done here.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  The contents of the file amsl-art.bbl follow:

\makeatletter \renewcommand{\@biblabel}[1]{\hfill#1.}\makeatother
%\newcommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\,}
\begin{thebibliography}{10}

\bibitem{AVG1}
V.~L. Arnol$'$d, A.~N. Varchenko, and S.~M. Gusein-Zade, {\em Singularities of
  differentiable maps. \rom{I}}, ``Nauka'', Moscow, 1982 (Russian), English
  transl., Birkh\"auser, Basel, 1985.

\bibitem{AVG2}
\bysame, {\em Singularities of differentiable maps. \rom{II}}, ``Nauka'',
  Moscow, 1984 (Russian), English transl., Birkh\"auser, Basel, 1988.

\bibitem{Art}
A.~M. Arthurs, {\em Complementary variational principles}, 2nd ed., Clarendon,
  Oxford, 1980.

\bibitem{BCW}
H.~Bass, E.~H. Connell, and D.~Wright, {\em The {J}acobian conjecture}, Bull.
  Amer. Math. Soc. {\bf 7} (1982), 287--330.

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

\bibitem{Ber}
V.~I. Berdichevski\u\i, {\em A variational equation of continuum mechanics},
  Problems of the Mechanics of a Solid Deformable Body (L.~I. Sedov and Yu.~N.
  Robotnov, eds.), ``Sudostroenie'', Leningrad, 1970, (V. V. Novozhilov
  Sixtieth Birthday Vol.), pp.~55--66 (Russian).

\bibitem{Coo1}
B.~Coomes, {\em Polynomial flows, symmetry groups, and conditions sufficient
  for injectivity of maps}, Ph.D. thesis, Univ. Nebraska--Lincoln, 1988.

\bibitem{Coo2}
\bysame, {\em The {L}orenz system does not have a polynomial flow}, J.
  Differential Equations (to appear).

\bibitem{Cot}
R.~W. Cottle et~al. (eds.), {\em Variational inequalities and complementarity
  problems}, Proc. Internat. School (Erice, 1978), Wiley, New York, 1980.

\bibitem{For}
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{Gab}
P.~Gabriel, {\em Unzerlegbare {D}arstellungen. \rom{II}}, Manuscripta Math.
  {\bf 6} (1972), 71--103.

\bibitem{GHMR}
J.~Guckenheimer, P.~Holmes, M.~Martineau, and L.~P. Robinson, {\em Nonlinear
  oscillations, dynamical systems, and bifurcations of vector fields},
  Springer-Verlag, New York, 1983.

\bibitem{HM}
S.~I. Hariharan and T.~H. Moulton (eds.), {\em Numerical methods for partial
  differential equations}, Longman, New York, 1986.

\bibitem{HS}
J.~K. Hunter and J.~Scheurie, {\em Perturbed solitary wave solutions of a model
  equation for water waves}, Physica D (to appear).

\bibitem{LL}
P.~D. Lax and C.~D. Levermore, {\em The small dispersion limit for the {KdV}
  equation. \rom{I (overview)}, \rom{II}, \rom{III}}, Comm. Pure Appl. Math.
  {\bf 36} (1983), 253--290, 571--594, 809--829.

\bibitem{Lio}
J.~L. Lions, {\em Probl\`emes mixtes abstraits}, Proc. Internat. Congr. Math.
  (Edinburgh, 1958), Cambridge Univ. Press, London and New York, 1960,
  pp.~389--397.

\bibitem{Mar}
A.~E. Martynyuk, {\em Some approximate methods for solving nonlinear equations
  with unbounded operators}, Izv. Vyssh. Uchebn. Zaved. Mat. {\bf 1966},
  no.~6(55), 85--94 (Russian), addendum, ibid. {\bf 1967} no. 8(63), 111.

\bibitem{Mei1}
G.~H. Meisters, {\em Jacobian problems in differential equations and algebraic
  geometry}, Rocky Mountain J. Math. {\bf 12} (1982), 679--705.

\bibitem{Mei2}
\bysame, {\em Polynomial flows on {$\bold R^n$}}, Proc. Semester on Dynamical
  Systems (Warsaw, Autumn 1986), Springer-Verlag, Berlin, Heidelberg, and New
  York, (to appear).

\bibitem{MO}
G.~H. Meisters and C.~Olech, {\em A poly-flow formulation of the {J}acobian
  conjecture}, Bull. Acad. Polon. Sci. S\'er. Sci. Math. {\bf 35} (1987),
  725--731.

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

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

\bibitem{Slo}
L.~N. Slobodetski\u\i, {\em Generalized {S}obolev spaces and their application
  to boundary value problems for partial differential equations}, Leningrad.
  Gos. Ped. Inst. Uchen. Zap. {\bf 197} (1958), 54--112 (Russian), English
  transl. in Amer. Math. Soc. Transl. (2) {\bf 57} (1966).

\bibitem{Spi}
M.~D. Spivak, {\em The joy of {\TeX}}, 2nd revised ed., Amer. Math. Soc.,
  Providence, R.~I., 1990.

\end{thebibliography}

%%  End of included file amsl-art.bbl.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

% [end of file amsl-art.tex]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%