Definable compactness in o-minimal structures

Abstract

We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types, and definable downward directed families of closed sets.

This is a round-up of the topological content of arXiv:2111.03802

References in corpus (2)

• Interpretable sets in dense o-minimal structures
• Definable compactness in definably complete locally o-minimal structures