Countably compact extensions and cardinal characteristics of the continuum
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917927664484352 |
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| author | Bardyla, Serhii Nyikos, Peter Zdomskyy, Lyubomyr |
| author_facet | Bardyla, Serhii Nyikos, Peter Zdomskyy, Lyubomyr |
| contents | In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$ if and only if every regular first-countable space of weight $< \mathfrak c$ can be densely embedded into a regular first-countable countably compact space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Countably compact extensions and cardinal characteristics of the continuum Bardyla, Serhii Nyikos, Peter Zdomskyy, Lyubomyr Logic General Topology In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$ if and only if every regular first-countable space of weight $< \mathfrak c$ can be densely embedded into a regular first-countable countably compact space. |
| title | Countably compact extensions and cardinal characteristics of the continuum |
| topic | Logic General Topology |
| url | https://arxiv.org/abs/2404.09004 |