On fuzzy pairwise - T0 and fuzzy pairwise - T1 bitopological spaces

Abstract

Fuzzy pairwise-Ti (in short FP-Ti , i = 0, 1) bitopological spaces have been introduced earlier by Kandil and El-Shafee3 , Safiya et al.10 and Kandil et al.2. Fuzzy pairwise-T0 separation axiom has also been introduced by Choubey1. Here we add two more definitions of fuzzy pairwise-Ti separation axioms each for i = 0, 1. In all we have studied seven possible definitions of FP-T0 and six possible definitions of FP-T1 spaces. All these definitions satisfy 'good extension' property. Among these defining cpncepts, we choose those definitions of FP-Ti (i = 0, 1) spaces viz., FP-T0 (i) and FP-T1 (i) which seem to be most appropriate according to out point of view. On comparing these definitions with the remaining ones, it turns out that FP-T0 (i) is the weakest and FP-T1, (i) is the strongest among all. Finally, we prove that FP-T1 (i) and FP- T1, (i) are hereditary, productive and projective properties.