Normal Spaces via Urysohn's Lemma as a Lifting Property

2026/01/21 by Robert Maxton · 1 voice
Mathematics · #math.GN

paper · pdf

Abstract

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 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.

Citations

• The unreasonable power of the lifting property in elementary mathematics

Discussions

• Robert Maxton: Normal Spaces via Urysohn's Lemma as a Lifting Property https://arxiv.org/abs/2602.11178 https://arxiv.org/pdf/2602.11178 https://arxiv.org/html/2602.11178 [bsky, 0 points, 0 comments]

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• H*-Normal Spaces and Some Related Functions
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