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 |
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Keywords
- Left adjoint
- Sober space
- Topological category
- Topological separation properties
ASJC Scopus subject areas
- Mathematics(all)
Cite this
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 journal › Article
}
TY - JOUR
T1 - Pre-Hausdorff spaces
AU - Stine, Jay
AU - Mielke, Marvin
PY - 2008/12/26
Y1 - 2008/12/26
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=57849147164&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=57849147164&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:57849147164
VL - 73
SP - 379
EP - 390
JO - Publicationes Mathematicae
JF - Publicationes Mathematicae
SN - 0033-3883
IS - 3-4
ER -