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 language | English (US) |
|---|---|
| Pages (from-to) | 379-390 |
| Number of pages | 12 |
| Journal | Publicationes Mathematicae |
| Volume | 73 |
| Issue number | 3-4 |
| State | Published - Dec 26 2008 |
| Externally published | Yes |
Keywords
- Left adjoint
- Sober space
- Topological category
- Topological separation properties
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
Stine, J., & Mielke, M. V. (2008). Pre-Hausdorff spaces. Publicationes Mathematicae, 73(3-4), 379-390.