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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17573 |
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| _version_ | 1866909405640916992 |
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| author | Hevessy, Michal |
| author_facet | Hevessy, Michal |
| contents | In this paper a construction of a metrizable zero-dimensional CDH space $X$ such that $X^2$ has exactly $\mathfrak{c}$ countable dense subsets is provided. Furthermore, it is shown that the space can be constructed consistently co-analytic. Thus answering an open question asked by Medini. To do so we use the notion of $λ$-sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH Hevessy, Michal General Topology 54G20 (Primary) 54H05 (Secondary) In this paper a construction of a metrizable zero-dimensional CDH space $X$ such that $X^2$ has exactly $\mathfrak{c}$ countable dense subsets is provided. Furthermore, it is shown that the space can be constructed consistently co-analytic. Thus answering an open question asked by Medini. To do so we use the notion of $λ$-sets. |
| title | Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH |
| topic | General Topology 54G20 (Primary) 54H05 (Secondary) |
| url | https://arxiv.org/abs/2411.17573 |