Definable one dimensional topologies in o-minimal structures

Ya'acov Peterzil; Ayala Rosel

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arXiv · 1807.08086

Definable one dimensional topologies in o-minimal structures

Ya'acov Peterzil·Ayala Rosel

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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.

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BibTeX RIS

Ya'acov Peterzil, Ayala Rosel. 2018-07-21. Definable one dimensional topologies in o-minimal structures. https://arxiv.org/abs/1807.08086

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