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