Proximal and Descriptive Topological Rings: Structure and Properties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915473183997952 |
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| author | Almahariq, Maram |
| author_facet | Almahariq, Maram |
| contents | The set of open subsets in a proximity space (X,ζ) forms a topological system that enables the definition of proximal and descriptive topological groups. This framework naturally extends to proximal and descriptive topological rings as well. In this study, I review fundamental properties and related results, with particular emphasis on the definition of proximal and descriptive fields. In addition, I examine the behavior of closed sets in proximal and descriptive topological rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proximal and Descriptive Topological Rings: Structure and Properties Almahariq, Maram Algebraic Topology 54E05, 54H05, 54E17, 22A20 The set of open subsets in a proximity space (X,ζ) forms a topological system that enables the definition of proximal and descriptive topological groups. This framework naturally extends to proximal and descriptive topological rings as well. In this study, I review fundamental properties and related results, with particular emphasis on the definition of proximal and descriptive fields. In addition, I examine the behavior of closed sets in proximal and descriptive topological rings. |
| title | Proximal and Descriptive Topological Rings: Structure and Properties |
| topic | Algebraic Topology 54E05, 54H05, 54E17, 22A20 |
| url | https://arxiv.org/abs/2509.01466 |