Quasi Separation Axioms

Authors: MOHAMMAD S. SARSAK

Abstract: In [5], Maheshwari et al. introduced and studied some new separation axioms, namely, quasi semi T_i axioms where i \in {0, 1, 2}, the quasi semi T_{1/2} axiom was then introduced and investigated by Gyu-Ihn et al. in [2]. In the present paper we introduce and study quasi T_i axioms, i \in {0, 1 / 2, 1, 2} as a special variety of quasi semi T_i axioms, the class of quasi T_{1/2} (respectively, quasi T_1) bitopological spaces is placed between quasi T_0 (respectively, quasi T_{1/2}) bitopological spaces and quasi T_1 (respectively, quasi T_2) bitopological spaces. Among several counter examples we introduce an example of a bitopological space which is quasi T_0 that fails to be quasi semi T_{1/2}, thus answering a question raised in [2].

Keywords: bitopological spaces, quasi open sets, quasi semi-open sets, quasi T_i, quasi semi T_i, i \in {0, 1 / 2, 1, 2}

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