English

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.

Keywords

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}
}
R2 v1 2026-06-23T16:34:42.731Z