Overview of Császár orders and quasi-uniformities on complete lattices

dc.contributor.authorBakulikira C, Iragi.
dc.date.accessioned2025-06-11T11:53:56Z
dc.date.available2025-06-11T11:53:56Z
dc.date.issued2025
dc.description.abstractIn 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.
dc.identifier.citationIragi, B.C., 2025. Overview of Császár orders and quasi-uniformities on complete lattices. Topology and its Applications, p.109229.
dc.identifier.issnhttps://doi.org/10.1016/j.topol.2025.109229
dc.identifier.urihttps://hdl.handle.net/10566/20481
dc.language.isoen
dc.publisherElsevier B.V.
dc.subjectClosure operator
dc.subjectInterior operator
dc.subjectLattice
dc.subjectQuasi-uniformity
dc.subjectSyntopogenous
dc.titleOverview of Császár orders and quasi-uniformities on complete lattices
dc.typeArticle

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