Normal Spaces via Urysohn's Lemma as a Lifting Property

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 $\mathbf{Top}$, 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.

3 pages, 6 figures, formalization in Lean in terms of existing definitions in Mathlib at https://github.com/robertmaxton42/mathlib4/tree/separation