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

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	English
Article number	1-2
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

Bibliographical note

DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

Keywords

Definable topology
One-dimensional topology
o-minimality

ASJC Scopus subject areas

Philosophy
Logic

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10.1007/s00153-019-00680-z

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N2 - 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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Definable one-dimensional topologies in O-minimal structures

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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