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arXiv · 2303.01644

Definable compactness in definably complete locally o-minimal structures

Masato Fujita
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Abstract

We demonstrate that And\'ujar Guerrero, Thomas and Walsberg's results on definable compactness in o-minimal structures still hold true in definably complete locally o-minimal structures. As an application, we show that a definably simple definable topological group which is regular, Hausdorff and definably compact as a definable topological space is either discrete or definably connected. We also study the definable quotient of definable continuous actions by definably compact definable topological groups.

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Masato Fujita. 2023-03-03. Definable compactness in definably complete locally o-minimal structures. https://doi.org/10.4064/fm230612-19-3

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