Submission date: 24 April 2024

Abstract:

Definable topological groups whose topologies are affine have definable 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.

Mathematics Subject Classification: Primary 03C64, Secondary 54H11

Keywords and phrases:

Full text arXiv 2404.15647: pdf, ps.