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On some separation axioms Mah, Peter Fritz

Abstract

Relations between pairs of separation axioms are considered. Given two separation axioms, it is investigated whether or not a topological space having the property of one of the separation axioms has the property of the other. Eighteen separation axioms are considered and the relation between the members of pairs of separation axioms is determined in every possible case. That is, with each pair of separation axioms there is associated a theorem showing the relative strengths of the members or an example showing their relative independence. As a secondary interest, some characterizations of most of the eighteen separation axioms are given. Also some necessary conditions for normal spaces and completely normal spaces are generalized.

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