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

Abstract

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.

Keywords

• $(\mu_i,\mu_j)$-adherence, $(\mu_i,\mu_j)$-convergence
• $\mu$-IFIP, net of $\mu$-open sets