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DIMENSION INEQUALITY FOR A DEFINABLY COMPLETE UNIFORMLY LOCALLY O-MINIMAL STRUCTURE OF THE SECOND KIND
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 85 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 07 September 2020, pp. 1654-1663
- Print publication:
- December 2020
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- Article
- Export citation
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Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let
$f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality 
$\dim (f(X)) \leq \dim (X)$ 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.
