Separation axioms on function spaces defined on bitopological spaces

Abstract

Inthispaper,wegeneralizeseparationaxiomstothefunctionspacep−Cω(Y ,Z)andstudyhowtheyrelate to separation axioms defined on the spaces (Z,δi) for i = 1,2, (Z,δ1,δ2), 1−Cς(Y ,Z) and 2−Cζ(Y ,Z). We show that the space p−Cω(Y ,Z) is pT◦, pT1, pT2 and pregular, if the spaces (Z,δ1) and (Z,δ2) are both T◦, T1, T2 andregularrespectively. Thespacep−Cω(Y ,Z)isalsoshowntobe pT◦, pT1, pT2 and pregular,ifthespace (Z,δ1,δ2) is p−T◦, p−T1, p−T2 and p-regular respectively. Finally, the space p−Cω(Y ,Z) is shown to be pT◦, pT1, pT2 and pregular, ifandonlyifthespaces1−Cς(Y ,Z)and2−Cζ(Y ,Z)arebothT0,T1,T2, andonly if the spaces 1−Cς(Y ,Z) and 2−Cζ(Y ,Z) are both regular respectively.