Weakly and Strongly Reversible Spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910737869307904 |
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| author | Kurilić, Miloš S. |
| author_facet | Kurilić, Miloš S. |
| contents | A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are condensations $f:{\mathcal X} \rightarrow {\mathcal Y}$ and $g:{\mathcal Y} \rightarrow {\mathcal X}$, there is a homeomorphism $h:{\mathcal X} \rightarrow {\mathcal Y}$; strongly reversible iff each bijection $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism. We show that the class of weakly reversible non-reversible spaces is disjoint from the class of sequential spaces in which each sequence has at most one limit (containing e.g. metrizable spaces). On the other hand, the class of strongly reversible topologies contains only discrete topologies, antidiscrete topologies and natural generalizations of the cofinite topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly and Strongly Reversible Spaces Kurilić, Miloš S. General Topology 54A10, 54C05, 54C10, 54D55 A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are condensations $f:{\mathcal X} \rightarrow {\mathcal Y}$ and $g:{\mathcal Y} \rightarrow {\mathcal X}$, there is a homeomorphism $h:{\mathcal X} \rightarrow {\mathcal Y}$; strongly reversible iff each bijection $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism. We show that the class of weakly reversible non-reversible spaces is disjoint from the class of sequential spaces in which each sequence has at most one limit (containing e.g. metrizable spaces). On the other hand, the class of strongly reversible topologies contains only discrete topologies, antidiscrete topologies and natural generalizations of the cofinite topology. |
| title | Weakly and Strongly Reversible Spaces |
| topic | General Topology 54A10, 54C05, 54C10, 54D55 |
| url | https://arxiv.org/abs/2412.07705 |