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arXiv · 1509.08484

Tame Topology over Dp-minimal Structures

Pierre Simon·Erik Walsberg
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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.

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Pierre Simon, Erik Walsberg. 2015-09-28. Tame Topology over Dp-minimal Structures. https://doi.org/10.1215/00294527-2018-0019

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