Definable one-dimensional topologies in O-minimal structures

Ya’acov Peterzil, Ayala Rosel

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)103-125
Number of pages23
JournalArchive for Mathematical Logic
Issue number1-2
StatePublished - 1 Feb 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.


  • Definable topology
  • One-dimensional topology
  • o-minimality

ASJC Scopus subject areas

  • Philosophy
  • Logic


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