On \mu^{*}-R_{۰} and \mu^{*}-R_{۱} Spaces with Separation Axioms

In this paper, we define and investigate \mu^{*}-R_{۰} and \mu^{*}-R_{۱} spaces in a generalized topological space together with a topology. Independence of these spaces from the existing allied concepts is shown by examples, which motivates to explore them further. It is interesting to note that (\mu X, \mu Y)-continuous image of \mu^{*}-R_{۰} space is neither \mu^{*}-R_{۰} nor \mu-R_{۰}. Further, conditions under which  the (\mu X, \mu Y)-continuous image of \mu^{*}-R_{۰} space becomes \mu^{*}-R_{۰} and \mu-R_{۰} are established. Also, some new versions of separation axioms are defined and they are used as a tool to investigate \mu^{*}-R_{۰} and \mu^{*}-R_{۱} spaces. Further,  the  conditions under which these spaces coincide are obtained.

Keywords:

μ∗-open(closed) map , μ∗-kernel , μ∗-T۰ , μ∗-T۱ , μ∗-T۲ spaces