The Kuratowski Closure-Complement Theorem

Peter Gammie and Gianpaolo Gioiosa

26 October 2017

Abstract

We discuss a topological curiosity discovered by Kuratowski (1922): the fact that the number of distinct operators on a topological space generated by compositions of closure and complement never exceeds 14, and is exactly 14 in the case of R. In addition, we prove a theorem due to Chagrov (1982) that classifies topological spaces according to the number of such operators they support.
BSD License

Topics

Theories