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References (9)
-
A. Pillay (1987)
First order topological structures and theoriesJournal of Symbolic Logic, 52
-
τ is regular, and (X , τ ) has finitely many definably connected components -
Will Johnson (2014)
Topologizing interpretable sets in O-minimal Structures -
D. Marker (2002)
Model theory : an introduction -
X , τ ) is definably homeomorphic to a definable set with its affine topology -
Erik Walsberg (2015)
On the Topology of Metric Spaces definable in o-minimal expansions of fieldsarXiv: Logic
-
L. Dries (1998)
Tame Topology and O-minimal Structures -
Y. Peterzil, C. Steinhorn (1999)
Definable Compactness and Definable Subgroups of o‐Minimal GroupsJournal of the London Mathematical Society, 59
-
A. Onshuus, C. Steinhorn (2009)
On linearly Ordered Structures of finite RankJ. Math. Log., 9
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2019
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-019-00680-z
- Publisher site
- See Article on Publisher Site
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\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( X,\tau \right) $$\end{document} is definably homeomorphic to an affine definable space (namely, a definable subset of Mn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M^{n}$$\end{document} 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.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Mar 2, 2020