Definable one-dimensional topologies in O-minimal structures

Ya’acov Peterzil; Ayala Rosel

doi:10.1007/s00153-019-00680-z

Definable one-dimensional topologies in O-minimal structures

Ya’acov Peterzil, Ayala Rosel

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

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	American English
Pages (from-to)	103-125
Number of pages	23
Journal	Archive for Mathematical Logic
Volume	59
Issue number	1-2
DOIs	https://doi.org/10.1007/s00153-019-00680-z
State	Published - 1 Feb 2020

Keywords

Definable topology
One-dimensional topology
o-minimality

All Science Journal Classification (ASJC) codes

Philosophy
Logic

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10.1007/s00153-019-00680-z

Cite this

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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 (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.",

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AB - 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.

KW - Definable topology

KW - One-dimensional topology

KW - o-minimality

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Definable one-dimensional topologies in O-minimal structures

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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