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.
|Number of pages||23|
|Journal||Archive for Mathematical Logic|
|State||Published - 1 Feb 2020|
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- Definable topology
- One-dimensional topology
ASJC Scopus subject areas