Definable \mathcal C^r structures on definable topological groups in d-minimal structures

2024/04/24 by Masato Fujita, Fujita, Masato
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Primary 03C64 #Rings, Modules, and Algebras #Secondary 54H11

paper · pdf · doi:10.48550/arxiv.2404.15647

openalex publication_date 2024/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Definable topological groups whose topologies are affine have definable \mathcal C^r structures in d-minimal expansions of ordered fields, where r is a positive integer. We prove this fact using a new notion called partition degree of a definable set. Basic properties of partition degree are also studied.

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