Definable compactness in o-minimal structures
Logic
2025-04-29 v2 General Topology
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.
Cite
@article{arxiv.2405.07112,
title = {Definable compactness in o-minimal structures},
author = {Pablo Andújar Guerrero},
journal= {arXiv preprint arXiv:2405.07112},
year = {2025}
}
Comments
This is a round-up of the topological content of arXiv:2111.03802