The Kuratowski Closure-Complement Theorem

Peter Gammie 🌐 and Gianpaolo Gioiosa

October 26, 2017

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

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.

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BSD License

Topics

Session Kuratowski_Closure_Complement

Cite

× 
@article{Kuratowski_Closure_Complement-AFP,
  author  = {Peter Gammie and Gianpaolo Gioiosa},
  title   = {The Kuratowski Closure-Complement Theorem},
  journal = {Archive of Formal Proofs},
  month   = {October},
  year    = {2017},
  note    = {\url{https://isa-afp.org/entries/Kuratowski_Closure_Complement.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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