Uniformity on generalized topological spaces
Purpose – The present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space. Design/methodology/approach – The existence of uniformity for a completely regular topological space is well-known, and the interr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2022-06-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2021-0058/full/pdf |
| Summary: | Purpose – The present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space. Design/methodology/approach – The existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks. Findings – It is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set. Originality/value – It is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces. |
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| ISSN: | 1319-5166 2588-9214 |