On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_712996_256cf6f6eacb48a30843ebd0f3b59d9c.pdf |
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| Summary: | 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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| ISSN: | 2322-5807 2423-3900 |