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| dc.contributor.supervisor | Mushaandja, Zechariah | |
| dc.contributor.author | Ramodimo, Tsie | |
| dc.date.accessioned | 2025-09-01T13:06:47Z | |
| dc.date.available | 2025-09-01T13:06:47Z | |
| dc.date.issued | 2022-11 | |
| dc.identifier.citation | Ramodimo,T. (2023) Permutable Pairs of Quasi-Uniformities. BIUST | en_US |
| dc.identifier.uri | https://repository.biust.ac.bw/handle/123456789/662 | |
| dc.description | Thesis (MSc of Mathematics and Statistical sciences)---Botswana International University of Science and Technology, 2023 | en_US |
| dc.description.abstract | In this project we study permutable pairs of quasi-uniformities. Our objective is to investigate the notion of permutability of quasi-uniformities in the context of conjugates, complements, adjacent and independent quasi-uniformities, following the work of authors like H. Weber, E.P de Jager and H.P.A. K¨unzi. The notion of quasi-uniformity which is a generalization of the concept of a uniformity is discussed in terms of surroundings. Two quasi-uniformities U and V on a set X are said to be permutable provided U ◦V = V◦U. Some characterizations of permutability are presented. Among other results, we show that conjugates of permutable quasi-uniformities permute and conjugates of adjacent quasi-uniformities are adjacent. Complementary quasi-uniformities are discussed and a connection between complementary quasi-uniformities and permutability is shown. Furthermore, the notion of independent quasi-uniformities is discussed. In particular we present a well known result from ([3], corollary 4) in terms of independent quasi- uniformities. Some useful examples are also discussed. | en_US |
| dc.description.sponsorship | Simons Foundation. | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Botswana International University of Science and Technology (BIUST) | en_US |
| dc.subject | Permutable pairs | en_US |
| dc.subject | Quasi-uniformities | en_US |
| dc.subject | Anti-atom | en_US |
| dc.subject | Topological space | en_US |
| dc.title | Permutable Pairs of Quasi-Uniformities | en_US |
| dc.description.level | msc | en_US |
| dc.description.accessibility | unrestricted | en_US |
| dc.description.department | mss | en_US |
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