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.

I corrected the author's name of a referred paper

References in corpus (1)

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

Cited by in corpus (1)

• Definable compactness in o-minimal structures