Pre-Hausdorff spaces

Jay Stine, M. V. Mielke

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper introduces three separation conditions for topological spaces, called T0,1, T0,2 ("pre-Hausdorff"), and T 1,2. These conditions generalize the classical T1 and T2 separation axioms, and they have advantages over them topologically which we discuss. We establish several different characterizations of pre-Hausdorff spaces, and a characterization of Hausdorff spaces in terms of pre-Hausdorff. We also discuss some classical Theorems of general topology which can or cannot be generalized by replacing the Hausdorff condition by pre-Hausdorff.

Original languageEnglish (US)
Pages (from-to)379-390
Number of pages12
JournalPublicationes Mathematicae
Issue number3-4
StatePublished - 2008
Externally publishedYes


  • Left adjoint
  • Sober space
  • Topological category
  • Topological separation properties

ASJC Scopus subject areas

  • Mathematics(all)


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