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arXiv · 0803.1175

Pre-Hausdorff Spaces

Jay Stine·M. V. Mielke
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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.

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Jay Stine, M. V. Mielke. 2008-03-07. Pre-Hausdorff Spaces. https://arxiv.org/abs/0803.1175

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