Compact spaces homeomorphic to their respective squares
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914642142429184 |
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| author | Dudák, Jan Vejnar, Benjamin |
| author_facet | Dudák, Jan Vejnar, Benjamin |
| contents | We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a family of size continuum of pairwise non-homeomorphic compact metrizable zero-dimensional spaces homeomorphic to their respective squares. This answers a question of W. J. Charatonik. We also discuss the situation in the classes of continua, Peano continua and absolute retracts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact spaces homeomorphic to their respective squares Dudák, Jan Vejnar, Benjamin General Topology 54F15, 54E45 We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a family of size continuum of pairwise non-homeomorphic compact metrizable zero-dimensional spaces homeomorphic to their respective squares. This answers a question of W. J. Charatonik. We also discuss the situation in the classes of continua, Peano continua and absolute retracts. |
| title | Compact spaces homeomorphic to their respective squares |
| topic | General Topology 54F15, 54E45 |
| url | https://arxiv.org/abs/2401.07633 |