Pre-Hausdorff Spaces
General Topology
2008-03-10 v1
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 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.
Keywords
Cite
@article{arxiv.0803.1175,
title = {Pre-Hausdorff Spaces},
author = {Jay Stine and M. V. Mielke},
journal= {arXiv preprint arXiv:0803.1175},
year = {2008}
}
Comments
10 pages