Normal Spaces via Urysohn's Lemma as a Lifting Property
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908828666167296 |
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| author | Maxton, Robert |
| author_facet | Maxton, Robert |
| contents | We present a translation of Urysohn's description of normal spaces (as those where disjoint closed subsets are separated by a continuous function) into the language of lifting properties in $\mathbf{Top}$, correcting a frequently-cited previous erroneous translation. We also present a translation of the definition of hereditarily normal spaces as those in which every open subspace is normal, by directly 'mapping' the translation of the usual description of normal spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normal Spaces via Urysohn's Lemma as a Lifting Property Maxton, Robert General Topology 54D15 (Primary) 18A20, 54B30 (Secondary) We present a translation of Urysohn's description of normal spaces (as those where disjoint closed subsets are separated by a continuous function) into the language of lifting properties in $\mathbf{Top}$, correcting a frequently-cited previous erroneous translation. We also present a translation of the definition of hereditarily normal spaces as those in which every open subspace is normal, by directly 'mapping' the translation of the usual description of normal spaces. |
| title | Normal Spaces via Urysohn's Lemma as a Lifting Property |
| topic | General Topology 54D15 (Primary) 18A20, 54B30 (Secondary) |
| url | https://arxiv.org/abs/2602.11178 |