English

Spaces where all bijections are morphisms

General Topology 2024-01-10 v1

Abstract

Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are continuous. Analogously, we classify all measurable spaces where all bijections to itself are measurable with measurable inverse. As a consequence, we also classify all measurable spaces where all maps to itself are measurable.

Keywords

Cite

@article{arxiv.2401.04381,
  title  = {Spaces where all bijections are morphisms},
  author = {Lucas H. R. de Souza},
  journal= {arXiv preprint arXiv:2401.04381},
  year   = {2024}
}

Comments

7 pages

R2 v1 2026-06-28T14:12:02.629Z