Locally o-minimal structures with tame topological properties

Abstract

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

References in corpus (1)

• Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind

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• Notes on definably complete locally o-minimal expansions of ordered groups
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