Locally o-minimal structures with tame topological properties
Logic
2023-02-22 v3
Abstract
We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.
Cite
@article{arxiv.2006.13481,
title = {Locally o-minimal structures with tame topological properties},
author = {Masato Fujita},
journal= {arXiv preprint arXiv:2006.13481},
year = {2023}
}