Notes on definably complete locally o-minimal expansions of ordered groups
arXiv:2204.01898 · doi:10.1002/malq.202200057
Abstract
We study definably complete locally o-minimal expansions of ordered groups in this paper. A definable continuous function defined on a closed, bounded and definable set behave like a continuous function on a compact set. We demonstrate uniform continuity of a definable continuous function on a closed, bounded and definable set and Arzela-Ascoli-type theorem. We propose a notion of special submanifolds with tubular neighborhoods and show that any definable set is decomposed into finitely many special submanifolds with tubular neighborhoods.
arXiv admin note: text overlap with arXiv:2010.02420