On the infinite powers of large zero-dimensional metrizable spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915447797972992 |
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| author | Medini, Andrea |
| author_facet | Medini, Andrea |
| contents | We show that $X^λ$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $λ$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the author. Along the way, we show that every non-compact weight-homogeneous metrizable space with a $π$-base consisting of clopen sets can be partitioned into $κ$ many clopen sets, where $κ$ is the weight of $X$. This improves a result of van Engelen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the infinite powers of large zero-dimensional metrizable spaces Medini, Andrea General Topology 54E35, 54B10, 54F45, 54F99 We show that $X^λ$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $λ$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the author. Along the way, we show that every non-compact weight-homogeneous metrizable space with a $π$-base consisting of clopen sets can be partitioned into $κ$ many clopen sets, where $κ$ is the weight of $X$. This improves a result of van Engelen. |
| title | On the infinite powers of large zero-dimensional metrizable spaces |
| topic | General Topology 54E35, 54B10, 54F45, 54F99 |
| url | https://arxiv.org/abs/2501.07253 |