Locally o-minimal open core

Abstract

We demonstrate that the open core of a definably complete expansion of a densely linearly ordered abelian group is locally o-minimal if and only if any definable closed subset of $R$ is either discrete or contains a nonempty open interval. Here, the notation $R$ denotes the universe of the original structure.

References in corpus (5)

• Locally o-minimal structures with tame topological properties
• Dimension inequality for a definably complete uniformly locally o-minimal structure of the second kind
• Tameness of definably complete locally o-minimal structures and definable bounded multiplication
• Almost o-minimal structures and $\mathfrak{X}$-structures
• Uniformly locally o-minimal open core