Abstract. In this paper, introducing various separation axioms on a bi-GTS, it has been observed that such separation axioms actually unify the well-known separation axioms on topological spaces. Several characterizations of such separation properties of a bi-GTS are established in terms of γ µ i ,µ j -closure operator, generalized cluster sets of functions and graph of functions.
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 respective categories. Descriptions of g-neighbourhood system, g-interior operator and subspaces of GTS alongwith a characterization of µ-T 1 -ness of a GTS in terms of g-quasi uniformity are established. Further, introducing g-quasi uniform isomorphism in a natural way, a couple of g-quasi uniform properties are also discussed.
In this paper, generalizations of adherence and convergence of nets and filters on a bi-GTS are introduced and studied. Several properties and interrelations among such adherence and convergence of nets and filters on a bi-GTS are discussed and characterized using graphs of functions. Finally, these results are applied to investigate the behaviour of a generalization of compactness, known as g ij -closedness of a bi-GTS.
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