Spaces where all bijections are morphisms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916085456961536 |
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| author | de Souza, Lucas H. R. |
| author_facet | de Souza, Lucas H. R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spaces where all bijections are morphisms de Souza, Lucas H. R. General Topology Primary: 54F65, 28A05, Secondary: 54A10, 54A25, 54C05 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. |
| title | Spaces where all bijections are morphisms |
| topic | General Topology Primary: 54F65, 28A05, Secondary: 54A10, 54A25, 54C05 |
| url | https://arxiv.org/abs/2401.04381 |