Pre-Hausdorff spaces
Copyright policy )Pre-Hausdorff spaces
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 T_(1) and T_(2) 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.
10 pages
- Misericordia University United States
- University System of Ohio United States
- Miami University United States
- University of Miami United States
topological category, left adjoint, General Topology (math.GN), 18B30; 54A05; 54D10, 54D10, Categories of topological spaces and continuous mappings, sober space, 54A05, reflective subcategory, Lower separation axioms (\(T_0\)--\(T_3\), etc.), pre-Hausdorff space, topological separation properties, 18B30, FOS: Mathematics, Categorical methods in general topology, Quotient spaces, decompositions in general topology, Mathematics - General Topology
topological category, left adjoint, General Topology (math.GN), 18B30; 54A05; 54D10, 54D10, Categories of topological spaces and continuous mappings, sober space, 54A05, reflective subcategory, Lower separation axioms (\(T_0\)--\(T_3\), etc.), pre-Hausdorff space, topological separation properties, 18B30, FOS: Mathematics, Categorical methods in general topology, Quotient spaces, decompositions in general topology, Mathematics - General Topology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!