Abstract
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.
Original language | English |
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Pages (from-to) | 103-125 |
Number of pages | 23 |
Journal | Archive for Mathematical Logic |
Volume | 59 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Feb 2020 |
Bibliographical note
Publisher Copyright:© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
- Definable topology
- One-dimensional topology
- o-minimality
ASJC Scopus subject areas
- Philosophy
- Logic