Pre-Hausdorff spaces

摘要

This paper introduces three separation conditions for topological spaces,called T_(0,1), T_(0,2)("pre-Hausdorff'), andT_(1,20.These conditions generalize the classicalT1and T2 separation axioms, and they have advantages over them topologically which wediscuss. We establish several different characterizations of pre-Hausdorff spaces, and acharacterization of Hausdorff spaces in terms of pre-Hausdorff. We also discuss someclassical Theorems of general topology which can or cannot be generalized by replacingthe Hausdorff condition by pre-Hausdorff.