Separation axioms on function spaces defined on bitopological spaces

Citation:
MUTURI NE, Khalagai JM, Pokhariyal GP. "Separation axioms on function spaces defined on bitopological spaces." Journal of Advanced Studies in Topology. 2018;9(2):113-118.

Abstract:

In this paper, we introduce separation axioms on the function space p− Cω(Y, Z) and study how they relateto separation axioms defined on the spaces (Z, δi) for i = 1, 2, (Z, δ1, δ2), 1 − Cς(Y, Z) and 2 − Cζ(Y, Z). Itis shown that the space p − Cω(Y, Z) is pT◦, pT1, pT2 and pregular, if the spaces (Z, δ1) and (Z, δ2) are bothT0, T1, T2 and regular respectively. The space p − Cω(Y, Z) is also shown to be pT0, pT1, pT2 and pregular,if the space (Z, δ1, δ2) is p − T0, p − T1, p − T2 and p-regular respectively. Finally, the space p − Cω(Y, Z) isshown to be pT0, pT1, pT2 and pregular, if and only if the spaces 1 − Cς(Y, Z) and 2 − Cζ(Y, Z) are both T0,T1, T2, and only if the spaces 1 − Cς(Y, Z) and 2 − Cζ(Y, Z) are both regular respectively.

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