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arXiv · 2204.01898

Notes on definably complete locally o-minimal expansions of ordered groups

Masato Fujita
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Abstract

We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate uniform continuity of a definable continuous function on a closed, bounded and definable set and Arzela-Ascoli-type theorem. We propose a notion of special submanifolds with tubular neighborhoods and show that any definable set is decomposed into finitely many special submanifolds with tubular neighborhoods.

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BibTeXRIS

Masato Fujita. 2022-04-04. Notes on definably complete locally o-minimal expansions of ordered groups. https://doi.org/10.1002/malq.202200057

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