Document Type : Research Paper
Authors
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.
Abstract
In this paper, we define and investigate $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ 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 $\mu^{*}$-$R_{0}$ space is neither $\mu^{*}$-$R_{0}$ nor $\mu$-$R_{0}$. Further, conditions under which the $(\mu X, \mu Y)$-continuous image of $\mu^{*}$-$R_{0}$ space becomes $\mu^{*}$-$R_{0}$ and $\mu$-$R_{0}$ are established. Also, some new versions of separation axioms are defined and they are used as a tool to investigate $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ spaces. Further, the conditions under which these spaces coincide are obtained.
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