The_Kuratowski_Closure-Complement_Theorem.pdf (305.71 kB)
The Kuratowski Closure-Complement Theorem
journal contribution
posted on 2023-05-16, 23:25 authored by Barry GardnerBarry Gardner, Jackson, MGThe Kuratowski Closure-Complement Theorem 1.1. [29] If (X; T) is a topo- logical space and A _ X then at most 14 sets can be obtained from A by taking closures and complements. Furthermore there is a space in which this bound is attained. This remarkable little theorem and related phenomena have been the concern of many authors. Apart from the mysterious appearance of the number 14, the attraction of this theorem is that it is simple to state and can be examined and proved using concepts available after any first encounter with topology. The goal of this article is both to provide an original investigation into variations of the theorem and its relation to properties of spaces and to survey the existing literature in this direction.
History
Publication title
New Zealand Journal of MathematicsVolume
38Pagination
9-44ISSN
1171-6096Department/School
School of Natural SciencesPublisher
New Zealand Mathematical Society and the Department of Mathematics of the University of Auckland.Place of publication
New ZealandRepository Status
- Open