### 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.

### License

BSD License

### Topics

- Mathematics/Topology

### Session Kuratowski_Closure_Complement

- KuratowskiClosureComplementTheorem

## Cite

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Kuratowski_Closure_Complement-AFP

    @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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