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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{http://isa-afp.org/entries/Kuratowski_Closure_Complement.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Status: [ok] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
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