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

Published online by Cambridge University Press:  07 September 2020

MASATO FUJITA*
Affiliation:
DEPARTMENT OF LIBERAL ARTS, JAPAN COAST GUARD ACADEMY, 5-1 WAKABA-CHO, KURE, HIROSHIMA737-8512, JAPANE-mail: [email protected]

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 the course of the proof of the inequality.

Type
Articles
Copyright
© The Association for Symbolic Logic 2020

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References

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