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arXiv · 2212.06401

Definable quotients in locally o-minimal structures

Masato Fujita·Tomohiro Kawakami
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Abstract

Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when $X$ is a locally closed definable subset of $F^n$ and there is a definable proper action of a definable group $G$ on $X$.

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Masato Fujita, Tomohiro Kawakami. 2022-12-13. Definable quotients in locally o-minimal structures. https://doi.org/10.1016/j.topol.2025.109479

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