Submission date: 8 February 2020.

Abstract:

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let f:X → R^n be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality dim(f(X)) ≤ dim(X) in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than dim(X). We also show that the structure is definably Baire in the course of the proof of the inequality.

Mathematics Subject Classification: Primary 03C64, Secondary 54F45, 54E52

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Full text arXiv 2002.03078: pdf, ps.