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arXiv · 2404.15647

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

Masato Fujita
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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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Masato Fujita. 2024-04-24. Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures. https://arxiv.org/abs/2404.15647

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