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

被引：7

作者：

Fujita, Masato ^{[1
]}

机构：

[1] Japan Coast Guard Acad, Dept Liberal Arts, 5-1 Wakaba Cho, Hiroshima 7378512, Japan

来源：

JOURNAL OF SYMBOLIC LOGIC | 2020年 / 85卷 / 04期

关键词：

uniformly locally o-minimal structure of the second kind; definably Baire structure; definably complete;

D O I：

10.1017/jsl.2020.31

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let f : X -> 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)) <= 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.

引用

页码：1654 / 1663

页数：10

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