Pre-Hausdorff spaces

Jay Stine; M. V. Mielke

Pre-Hausdorff spaces

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

Abstract

This paper introduces three separation conditions for topological spaces, called T_0,1, T_0,2 ("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 language	English (US)
Pages (from-to)	379-390
Number of pages	12
Journal	Publicationes Mathematicae
Volume	73
Issue number	3-4
State	Published - 2008
Externally published	Yes

Keywords

Left adjoint
Sober space
Topological category
Topological separation properties

ASJC Scopus subject areas

Mathematics(all)

Cite this

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AB - 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.

KW - Left adjoint

KW - Sober space

KW - Topological category

KW - Topological separation properties

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Pre-Hausdorff spaces

Abstract

Keywords

ASJC Scopus subject areas

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