# DIMENSION INEQUALITY FOR A DEFINABLY COMPLETE UNIFORMLY LOCALLY O-MINIMAL STRUCTURE OF THE SECOND KIND

@article{Fujita2020DIMENSIONIF, title={DIMENSION INEQUALITY FOR A DEFINABLY COMPLETE UNIFORMLY LOCALLY O-MINIMAL STRUCTURE OF THE SECOND KIND}, author={Masato Fujita}, journal={The Journal of Symbolic Logic}, year={2020}, volume={85}, pages={1654 - 1663} }

Abstract 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…

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