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Variations on Kuratowski's 14-set theorem

David Sherman
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Abstract

Kuratowski's 14-set theorem says that in a topological space, 14 is the maximum possible number of distinct sets which can be generated from a fixed set by taking closures and complements. In this article we consider the analogous questions for any possible subcollection of the operations {closure, complement, interior, intersection, union}, and any number of initially given sets. We use the algebraic "topological calculus" to full advantage.

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David Sherman. 2004-05-21. Variations on Kuratowski's 14-set theorem. https://arxiv.org/abs/math/0405401

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