Definable compactness in definably complete locally o-minimal structures

Abstract

We demonstrate that Andújar 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.

arXiv commentI corrected the author's name of a referred paper

References in corpus (3)

• Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind
• Tameness of definably complete locally o-minimal structures and definable bounded multiplication
• Notes on definably complete locally o-minimal expansions of ordered groups

Cited by in corpus (1)

• Definable compactness in o-minimal structures