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.

中文翻译：

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第二类可定义完整的局部 O-最小结构的维数不等式

考虑第二类稠密线性有序阿贝尔群的可定义完全均匀局部 o-极小展开。让$f:X \rightarrow R^n$是一个可定义的映射，其中X是一个可定义的集合并且R是结构的宇宙。我们证明了不等式$\dim (f(X)) \leq \dim (X)$在本文中。作为推论，我们得到点的集合F是不连续的 尺寸小于$\暗淡 (X)$. 我们还证明了在证明不等式的过程中，该结构可以定义为 Baie。