Separation axioms on function spaces defined on bitopological spaces

Main Article Content

N. E. Muturi
J. M. Khalagai
G. P. Pokhariyal

Abstract

In this paper, we introduce separation axioms on the function space pCω(Y, Z) and study how they relate
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). It
is shown that the space p Cω(Y, Z) is pT, pT1, pT2 and pregular, if the spaces (Z, δ1) and (Z, δ2) are both
T0, 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) is
shown 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.

Article Details

How to Cite
Muturi, N., Khalagai, J., & Pokhariyal, G. (2018). Separation axioms on function spaces defined on bitopological spaces. Journal of Advanced Studies in Topology, 9(2), 113-118. https://doi.org/10.20454/jast.2018.1454
Section
Original Articles