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2019 Tame Topology over dp-Minimal Structures
Pierre Simon, Erik Walsberg
Notre Dame J. Formal Logic 60(1): 61-76 (2019). DOI: 10.1215/00294527-2018-0019

Abstract

In this article, 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 “multivalued functions.” This generalizes known statements about weakly o-minimal, C-minimal, and P-minimal theories.

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Pierre Simon. Erik Walsberg. "Tame Topology over dp-Minimal Structures." Notre Dame J. Formal Logic 60 (1) 61 - 76, 2019. https://doi.org/10.1215/00294527-2018-0019

Information

Received: 1 November 2015; Accepted: 15 November 2016; Published: 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07060308
MathSciNet: MR3911106
Digital Object Identifier: 10.1215/00294527-2018-0019

Subjects:
Primary: 03C68

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 1 • 2019
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