On generalized cluster sets of functions and multifunctions

On $g_{ij}$-closed bi-generalized topological spaces

“…In continuation of our work on bi-generalized topological spaces (in short, bi-GTS) [2,1], we introduce and study certain generalizations of adherence and convergence of nets and filters on a bi-GTS. Discussing several properties and interrelations among such adherence and convergence of nets and filters on a bi-GTS, we have characterized them using graphs of functions.…”

“…Discussing several properties and interrelations among such adherence and convergence of nets and filters on a bi-GTS, we have characterized them using graphs of functions. Finally, the results obtained in the first part of the paper are applied to investigate the behaviour of a generalization of compactness, called g ij -closedness [2] of a bi-GTS.…”

Separation Axioms on Bi-Generalized Topological Spaces

“…Császár and and E.Makai Jr. in [5]. We study certain separation axioms on bi-GTS and find their characterizations in terms of γ µ i ,µ j -closure operator [5], graph of a function and generalized cluster sets [2] of a function. It is worth noting that the well-known separation axioms of bi-topological and hence topological spaces, follow as special cases for suitable choices of the bi-GTs.…”

“…It is worth noting that the well-known separation axioms of bi-topological and hence topological spaces, follow as special cases for suitable choices of the bi-GTs. In the next section, we investigate the behaviour of a bi-GTS obeying separation properties, in terms of a generalized closure operator called γ µ i ,µ j -closure operator [5]; while in the last section, a bi-GTS under separation properties are discussed in the light of graph of a function and generalized cluster sets [2] of a function. We now state certain useful definitions and quote several existing results that we require in the next two sections.…”