Magister Scientiae - MSc (Mathematics and Applied Mathematics)

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Overview of Császár orders and quasi-uniformities on complete lattices
(Elsevier B.V., 2025) Bakulikira C, Iragi.
In this paper we introduce a theory of quasi-uniformities and syntopogenous structures on complete lattices, extending the results from [7] and [5] in a general categorical context. In particular, we show that topogenous orders on a complete lattice encompass both closure and interior operations, and that a syntopogenous structure is a base of a quasi-uniformity. In fact, not only does this paper extend various structures from category theory, but it also demonstrates that these constructs can be studied without relying on (E,M)-factorizations, which have historically been necessary for their study in a categorical setting. In closing, we show that any ⋀-structure of a complete lattice can be used to construct a base of transitive quasi-uniformity on the lattice. © 2025 Elsevier B.V.