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.
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}
}
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7 pages