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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.05949 |
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| _version_ | 1866911573883224064 |
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| author | Kuba, Gerald |
| author_facet | Kuba, Gerald |
| contents | Let c denote the cardinality of the continuum. Let L denote the family of all Hausdorff topologies on the real line coarser than the natural topology. We construct 2^c pairwise non-homeomorphic completely normal topologies in L among which 2^c are Baire and 2^c are of first category. We also construct c pairwise non-homeomorphic completely metrizable topologies in L. Furthermore, we investigate complete lattices of topologies in L and construct extremely long chains of homeomorphic topologies in L. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05949 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Many coarse topologies on the real line Kuba, Gerald General Topology 54A525, 54D20, 54D05 Let c denote the cardinality of the continuum. Let L denote the family of all Hausdorff topologies on the real line coarser than the natural topology. We construct 2^c pairwise non-homeomorphic completely normal topologies in L among which 2^c are Baire and 2^c are of first category. We also construct c pairwise non-homeomorphic completely metrizable topologies in L. Furthermore, we investigate complete lattices of topologies in L and construct extremely long chains of homeomorphic topologies in L. |
| title | Many coarse topologies on the real line |
| topic | General Topology 54A525, 54D20, 54D05 |
| url | https://arxiv.org/abs/2604.05949 |