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Sierpinski's most important work is in the area of set theory, point set topology and number theory. In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.
He studied the Sierpinski curve which describes a closed path which contains every interior point of a square. The length of the curve is infinity, while the area enclosed by it is 5/12 that of the square.
Sierpinski was the author of 724 papers and 50 books.
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