An Approach to Change the Topology of a Topological Space
In this paper, we are going to introduce an approach to convert the topology of a topological space to another topology (in fact, a coarser topology). For this purpose, we consider a topological space $(X, \tau)$ with a closed point $p$ of its points. Using a grill $\mathcal{G}$ on the space $(...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2022-09-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_254339_7e881e561c422471177c3588c1ac0ca6.pdf |
| _version_ | 1811180281038635008 |
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| author | Amin Talabeigi Maryam Talabeigi |
| author_facet | Amin Talabeigi Maryam Talabeigi |
| author_sort | Amin Talabeigi |
| collection | DOAJ |
| description | In this paper, we are going to introduce an approach to convert the topology of a topological space to another topology (in fact, a coarser topology). For this purpose, we consider a topological space $(X, \tau)$ with a closed point $p$ of its points. Using a grill $\mathcal{G}$ on the space $(X, \tau)$ and the closure operator associated with $\tau$, we define a Kuratowski closure operator $cl^*_p$ on $X$ to create the desired topology. We then characterize the form of this resulting topology and also determine its relationship to the initial topology of the space. |
| first_indexed | 2024-04-11T06:48:46Z |
| format | Article |
| id | doaj.art-15448c46e4f34d3b8026f61a275dd8b2 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-11T06:48:46Z |
| publishDate | 2022-09-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-15448c46e4f34d3b8026f61a275dd8b22022-12-22T04:39:17ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002022-09-01193556310.22130/scma.2022.132038.842254339An Approach to Change the Topology of a Topological SpaceAmin Talabeigi0Maryam Talabeigi1Department of Mathematics, Payame Noor University(PNU), P.O.Box, 19395-4697, Tehran, Iran.Department of Electrical Computer Engineering, instructor of girls Kosar Sirjan branch, Technical and Vocational University (TVU), Kerman, Iran.In this paper, we are going to introduce an approach to convert the topology of a topological space to another topology (in fact, a coarser topology). For this purpose, we consider a topological space $(X, \tau)$ with a closed point $p$ of its points. Using a grill $\mathcal{G}$ on the space $(X, \tau)$ and the closure operator associated with $\tau$, we define a Kuratowski closure operator $cl^*_p$ on $X$ to create the desired topology. We then characterize the form of this resulting topology and also determine its relationship to the initial topology of the space.https://scma.maragheh.ac.ir/article_254339_7e881e561c422471177c3588c1ac0ca6.pdfkuratowski closure operatorgrillcoarster topologyextension topologyone-point extension topology |
| spellingShingle | Amin Talabeigi Maryam Talabeigi An Approach to Change the Topology of a Topological Space Sahand Communications in Mathematical Analysis kuratowski closure operator grill coarster topology extension topology one-point extension topology |
| title | An Approach to Change the Topology of a Topological Space |
| title_full | An Approach to Change the Topology of a Topological Space |
| title_fullStr | An Approach to Change the Topology of a Topological Space |
| title_full_unstemmed | An Approach to Change the Topology of a Topological Space |
| title_short | An Approach to Change the Topology of a Topological Space |
| title_sort | approach to change the topology of a topological space |
| topic | kuratowski closure operator grill coarster topology extension topology one-point extension topology |
| url | https://scma.maragheh.ac.ir/article_254339_7e881e561c422471177c3588c1ac0ca6.pdf |
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