On Generalized Quasi-uniformity and Generalized Quasi-uniformizable supratopological spaces

  title={On Generalized Quasi-uniformity and Generalized Quasi-uniformizable supratopological spaces},
  author={Atasi Deb Ray and Rakesh Bhowmick},
  journal={Journal of Advanced Studies in Topology},
In this paper, introducing generalized quasi uniformity (in short, \(g\)-quasi uniformity) and \(g\)-quasi uniformly continuous maps, it has been shown that every supratopology is achievable from a \(g\)-quasi uniformity; moreover, a \(g\)-continuous map between a pair of supratopological spaces is indeed the induced map obtained from the \(g\)-quasi uniformly continuous map between the corresponding \(g\)-quasi uniform spaces. These results establish a functorial correspondence between the… 
Product of generalized quasi-uniform spaces
In this paper, we introduce product \(g\)-quasi uniformity and show that product \(g\)-quasi uniformity induces the generalized product topology. We also provide a necessary and sucient condition for
Generalized quasi-uniformity in terms of covers
Recently g-quasi uniformity has been introduced, and in the literature there al- ready is the notion of strong quasi-uniform cover for quasi-uniform spaces. Here in this paper we generalize the
Uniformity on generalized topological spaces
PurposeThe 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/approachThe


The concept of generalized open sets in generalized topological spaces was introduced by A. Csaszar [6,7]. In this paper, we introduce the concept of γ*-semi-open sets and investigate the related
Generalized topology, generized continuity
The paper defines, with the help of generalized topologies and generalized neighbourhood systems, two kinds of generalized continuity, by giving in this way a general form to various concepts
Quasi-uniformization of topological spaces
On pre - continuous and week precontinuous mappings
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