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Functions Definable in Definably Complete Uniformly Locally O-minimal Structure of the Second Kind by Fujita, Masato is a scholarly article available to read on EtoBox.

What is Functions Definable in Definably Complete Uniformly Locally O-minimal Structure of the Second Kind about?

We investigate continuous functions definable in a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group (DCULOAS structure). We prove a variant of the Arzela-Ascoli theorem for uniformly continuous definable functions and the following assertion: Consider the parameterized function $f:C \times P \rightarrow M$ which is equi-continuous with respect to $P$. The projection image of the set at which $f$ is discontinuous to the parameter space $P$ is of dimension smaller than $\dim P$ when $C$ is closed and bounded. In addition, we demonstrate that an archimedean DCULOAS structure which enjoys definable Tietze extension property is o-minimal. In the appendix, we show that an o-minimal expansion of an ordered group is not semi-bounded if and only if it enjoys definable Tietze extension property.

Author

Fujita, Masato

Published

2020

Language

EN