Definable one dimensional topologies in o-minimal structures

Abstract

We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau \right)$ is definably homeomorphic to an affine definable space (namely, a definable subset of $M^n$ with the induced subspace topology). One of the main results says that it is sufficient for $X$ to be regular and decompose into finitely many definably connected components.

References in corpus (1)

• On the Topology of Metric Spaces definable in o-minimal expansions of fields