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

@article{Fujita2020DIMENSIONIF,
  title={DIMENSION INEQUALITY FOR A DEFINABLY COMPLETE UNIFORMLY LOCALLY O-MINIMAL STRUCTURE OF THE SECOND KIND},
  author={Masato Fujita},
  journal={The Journal of Symbolic Logic},
  year={2020},
  volume={85},
  pages={1654 - 1663}
}
  • M. Fujita
  • Published 8 February 2020
  • Computer Science, Mathematics
  • The Journal of Symbolic Logic
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… 
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