Tame Topology over Dp-minimal Structures
Logic
2019-09-18 v2
Abstract
We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous "multi-valued functions". This generalizes known statements about weakly o-minimal, C-minimal and P-minimal theories.
Cite
@article{arxiv.1509.08484,
title = {Tame Topology over Dp-minimal Structures},
author = {Pierre Simon and Erik Walsberg},
journal= {arXiv preprint arXiv:1509.08484},
year = {2019}
}
Comments
14 pages, some minor errors fixed