Pre-Hausdorff spaces

Jay Stine, Marvin Mielke

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume73
Issue number3-4
StatePublished - Dec 26 2008
Externally publishedYes

Fingerprint

Hausdorff space
Separation Axioms
Topological space
Topology
Generalise
Theorem

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Stine, J., & Mielke, M. (2008). Pre-Hausdorff spaces. Publicationes Mathematicae, 73(3-4), 379-390.

Pre-Hausdorff spaces. / Stine, Jay; Mielke, Marvin.

In: Publicationes Mathematicae, Vol. 73, No. 3-4, 26.12.2008, p. 379-390.

Research output: Contribution to journalArticle

Stine, J & Mielke, M 2008, 'Pre-Hausdorff spaces', Publicationes Mathematicae, vol. 73, no. 3-4, pp. 379-390.
Stine J, Mielke M. Pre-Hausdorff spaces. Publicationes Mathematicae. 2008 Dec 26;73(3-4):379-390.
Stine, Jay ; Mielke, Marvin. / Pre-Hausdorff spaces. In: Publicationes Mathematicae. 2008 ; Vol. 73, No. 3-4. pp. 379-390.
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