# The Kuratowski Closure-Complement Theorem

 Title: The Kuratowski Closure-Complement Theorem Authors: Peter Gammie and Gianpaolo Gioiosa Submission date: 2017-10-26 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. BibTeX: @article{Kuratowski_Closure_Complement-AFP, author = {Peter Gammie and Gianpaolo Gioiosa}, title = {The Kuratowski Closure-Complement Theorem}, journal = {Archive of Formal Proofs}, month = oct, year = 2017, note = {\url{https://isa-afp.org/entries/Kuratowski_Closure_Complement.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License