Topometric characterization of type spaces in continuous logic

2021/06/24 by James Hanson, Hanson, James
Mathematics · #03C66 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2106.13261

openalex publication_date 2021/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a topometric space X is topometrically isomorphic to a type space of some continuous first-order theory if and only if X is compact and has an open metric (i.e., satisfies that \p : d(p,U) < ε\ is open for every open U and ε > 0). Furthermore, we show that this can always be accomplished with a stable theory.

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