eCite Digital Repository

The Kuratowski Closure-Complement Theorem

Citation

Gardner, BJ and Jackson, MG, The Kuratowski Closure-Complement Theorem, New Zealand Journal of Mathematics, 38, (1) pp. 9-44. ISSN 1171-6096 (2008) [Refereed Article]


Preview
PDF
306Kb
  

Official URL: http://www.math.waikato.ac.nz/NZMS/NZMS.html

Abstract

The 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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Topology
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Gardner, BJ (Dr Barry Gardner)
ID Code:56054
Year Published:2008
Deposited By:Mathematics
Deposited On:2009-03-24
Last Modified:2011-11-02
Downloads:1,229 View Download Statistics

Repository Staff Only: item control page