The Kuratowski Closure-Complement Theorem

Peter Gammie 🌐 and Gianpaolo Gioiosa

October 26, 2017

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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


Session Kuratowski_Closure_Complement