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Preprint Number 1852
1852. Masato Fujita Functions definable in definably complete uniformly locally o-minimal
structure of the second kind E-mail: Submission date: 6 October 2020 Abstract: We consider a definably complete uniformly locally o-minimal expansion
of the
second kind of a densely linearly ordered abelian group (DCULOAS
structure) in
this paper. The first main theorem is the following monotonicity
theorem. For a
definable function f on an interval I, the interval I is
decomposed into
four definable sets. Three sets are open definable sets on which f is
locally
constant, locally strictly increasing and continuous, and locally strictly
decreasing and continuous, respectively. The last definable set is
discrete and
closed. Mathematics Subject Classification: 03C64 Keywords and phrases: |

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