We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space (X, τ) is definably homeomorphic to an affine definable space (namely, a definable subset of Mn 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.
Bibliographical notePublisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
- Definable topology
- One-dimensional topology
ASJC Scopus subject areas