Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures
Logic
2024-07-24 v2
Abstract
Definable topological groups whose topologies are affine have definable structures in d-minimal expansions of ordered fields, where 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.
Cite
@article{arxiv.2404.15647,
title = {Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures},
author = {Masato Fujita},
journal= {arXiv preprint arXiv:2404.15647},
year = {2024}
}