Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$beadefinablemap,where$X$isadefinablesetand$R$ is the universe of the structure. We demonstrate the inequality $\dim (f(X))\le \dim (X)$ 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 defiably Baire in the course of the proof of the inequality.