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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 conditionsgeneralize the classical T 1 and T 2 separation axioms, and they haveadvantages over them topologically which we discuss. We establish severaldifferent characterizations of pre-Hausdorff spaces, and a characterization ofHausdorff spaces in terms of pre-Hausdorff. We also discuss some classicalTheorems of general topology which can or cannot be generalized by replacingthe Hausdorff condition by pre-Hausdorff.



Author: Jay Stine, M.V. Mielke

Source: https://arxiv.org/







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