Kuratowski Monoids of n-Topological Spaces

Abstract

Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set X endowed with n pairwise comparable topologies Ʈ1 ⊂ · · · ⊂ Ʈn, by repeated application of the operations of complement and closure in the topologies Ʈ1, . . . , Ʈn to a subset A ⊂ X we can obtain at most

Keywords

• kuratowski monoid
• polytopological space
• n-topological space
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