On the Topology $τ_R^{\diamond}$ of Primal Topological Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914677726904320 |
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| author | Özkoç, Murad Köstel, Büşra |
| author_facet | Özkoç, Murad Köstel, Büşra |
| contents | The main purpose of this paper is to introduce and study two new operators $(\cdot)_R^{\diamond}$ and $cl_R^{\diamond}(\cdot)$ via primal which is a new notion. We also show that the operator $cl_R^{\diamond}(\cdot)$ is a Kuratowski closure operator, while the operator $(\cdot)_R^{\diamond}$ is not. In addition, we prove that the topology on $X$, shown as $τ_R^{\diamond},$ obtained by means of the operator $cl_R^{\diamond}(\cdot)$ is finer than $τ_δ,$ where $τ_δ$ is the family of $δ$-open subsets of a space $(X,τ).$ Moreover, we not only obtain a base for the topology $τ_R^{\diamond}$ but also prove many fundamental results concerning this new structure. Furthermore, we give many counterexamples related to our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Topology $τ_R^{\diamond}$ of Primal Topological Spaces Özkoç, Murad Köstel, Büşra General Topology 54A05, 54B99, 54C60 The main purpose of this paper is to introduce and study two new operators $(\cdot)_R^{\diamond}$ and $cl_R^{\diamond}(\cdot)$ via primal which is a new notion. We also show that the operator $cl_R^{\diamond}(\cdot)$ is a Kuratowski closure operator, while the operator $(\cdot)_R^{\diamond}$ is not. In addition, we prove that the topology on $X$, shown as $τ_R^{\diamond},$ obtained by means of the operator $cl_R^{\diamond}(\cdot)$ is finer than $τ_δ,$ where $τ_δ$ is the family of $δ$-open subsets of a space $(X,τ).$ Moreover, we not only obtain a base for the topology $τ_R^{\diamond}$ but also prove many fundamental results concerning this new structure. Furthermore, we give many counterexamples related to our results. |
| title | On the Topology $τ_R^{\diamond}$ of Primal Topological Spaces |
| topic | General Topology 54A05, 54B99, 54C60 |
| url | https://arxiv.org/abs/2402.08572 |