The number of complements of a topology on n points is at least 2n (except for some special cases)

Brown, Jason I.
Watson, Stephen

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Publication date

June 1996

DOI

10.1016/0012-365X(95)00004-G

Publisher

Published by Elsevier B.V.

ISSN

0012-365X

Abstract

AbstractWe improve the results of Hartmanis (1958) and Schnare (1968,1969) by showing that, if n ⩾ 4, then any topological space on n points (equivalently, any preordered set on n points) which is not in a certain short list has at least 2n complements. We have evaluated the exact number of complements of each of the topologies in the short list

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The number of complements of a topology on n points is at least 2n (except for some special cases)

Abstract

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The number of complements of a topology on n points is at least 2n (except for some special cases)

Abstract

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