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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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_712996_256cf6f6eacb48a30843ebd0f3b59d9c.pdf |
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| author | Pankaj Chettri Bishal Bhandari |
| author_facet | Pankaj Chettri Bishal Bhandari |
| author_sort | Pankaj Chettri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7cc3007d91ed493abee1e12ffd70509b |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-7cc3007d91ed493abee1e12ffd70509b2025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121341742910.22130/scma.2024.2012037.1469712996On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation AxiomsPankaj Chettri0Bishal Bhandari1Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpoo East Sikkim, India.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.https://scma.maragheh.ac.ir/article_712996_256cf6f6eacb48a30843ebd0f3b59d9c.pdfμ∗-open(closed) mapμ∗-kernelμ∗-t0μ∗-t1μ∗-t2 spaces |
| spellingShingle | Pankaj Chettri Bishal Bhandari On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms Sahand Communications in Mathematical Analysis μ∗-open(closed) map μ∗-kernel μ∗-t0 μ∗-t1 μ∗-t2 spaces |
| title | On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms |
| title_full | On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms |
| title_fullStr | On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms |
| title_full_unstemmed | On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms |
| title_short | On $\mu^{*}$-$R_{0}$ and $\mu^{*}$-$R_{1}$ Spaces with Separation Axioms |
| title_sort | on mu r 0 and mu r 1 spaces with separation axioms |
| topic | μ∗-open(closed) map μ∗-kernel μ∗-t0 μ∗-t1 μ∗-t2 spaces |
| url | https://scma.maragheh.ac.ir/article_712996_256cf6f6eacb48a30843ebd0f3b59d9c.pdf |
| work_keys_str_mv | AT pankajchettri onmur0andmur1spaceswithseparationaxioms AT bishalbhandari onmur0andmur1spaceswithseparationaxioms |