Normality in the square of the Sorgenfrey Line
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917424155066368 |
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| author | Szeptycki, Paul Wen, Hongwei |
| author_facet | Szeptycki, Paul Wen, Hongwei |
| contents | We consider sets of reals $X$ endowed with the Sorgenfrey lower limit topology denoted $X[\leq]$. Przymusiński proved that if $X$ is a $Q$-set then $(X[\leq])^2$ is normal. While the converse is not in general true we consider examples of sets of the reals for which $(X[\leq])^2$ is normal or just pseudo-normal. For example, if $X$ is a $λ$ set, then $(X[\leq])^2$ is pseudo-normal but assuming CH there is an $X$ concentrated on a countable dense subset (so not a $λ$-set) but still $(X[\leq])^2$ is normal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normality in the square of the Sorgenfrey Line Szeptycki, Paul Wen, Hongwei General Topology 54D15 We consider sets of reals $X$ endowed with the Sorgenfrey lower limit topology denoted $X[\leq]$. Przymusiński proved that if $X$ is a $Q$-set then $(X[\leq])^2$ is normal. While the converse is not in general true we consider examples of sets of the reals for which $(X[\leq])^2$ is normal or just pseudo-normal. For example, if $X$ is a $λ$ set, then $(X[\leq])^2$ is pseudo-normal but assuming CH there is an $X$ concentrated on a countable dense subset (so not a $λ$-set) but still $(X[\leq])^2$ is normal. |
| title | Normality in the square of the Sorgenfrey Line |
| topic | General Topology 54D15 |
| url | https://arxiv.org/abs/2511.12327 |