Semi-proximal spaces and normality
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911760691232768 |
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| author | Almontashery, Khulod Szeptycki, Paul |
| author_facet | Almontashery, Khulod Szeptycki, Paul |
| contents | We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a question of Nyikos. One of the examples is a subspace of $(ω+1) \times ω_1$. In contrast, we show that every normal subspace of a finite power of $ω_1$ is semi-proximal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00539 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-proximal spaces and normality Almontashery, Khulod Szeptycki, Paul General Topology Logic 54D15, 54G20 (Primary) 03E75, 03E05, 54B10, 54D15, 54D80 (Secondary) We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a question of Nyikos. One of the examples is a subspace of $(ω+1) \times ω_1$. In contrast, we show that every normal subspace of a finite power of $ω_1$ is semi-proximal. |
| title | Semi-proximal spaces and normality |
| topic | General Topology Logic 54D15, 54G20 (Primary) 03E75, 03E05, 54B10, 54D15, 54D80 (Secondary) |
| url | https://arxiv.org/abs/2311.00539 |