论文标题
第二种局部均匀局部O最小结构的维度不等式
Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind
论文作者
论文摘要
考虑第二种密度线性有序的Abelian群的明确完整的局部O-最低膨胀。令$ f：x \ rightarrow r^n $为可定义的地图，其中$ x $是可定义的集合，$ r $是结构的宇宙。我们在本文中演示了不等式$ \ dim（f（x））\ leq \ dim（x）$。作为推论，我们得到$ f $不连续的点的集合小于$ \ dim（x）$。我们还表明，在不平等的证明过程中，该结构是明确的。
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 defiably Baire in the course of the proof of the inequality.
