Submission date: 13 June 2024

Abstract:

We show that the 1-h-minimal fields satisfy a property of naive compactness for decreasing definable families of closed bounded sets indexed by the value group. We use this to prove that a local topological definable group has a definable family of neighborhoods of the identity consisting of open subgroups.

Mathematics Subject Classification: 03C07

Keywords and phrases:

Full text arXiv 2406.09249: pdf, ps.