Functions on $n$-generalized Topological Spaces

Abstract

An $n$-generalized topological ($n$-GT) space is a pair $(X,\mathscr{G})$ of a nonempty set $X$ and a collection $\mathscr{G}$ of $n$ $(n\in\mathbb{N})$ distinct generalized topologies (in the sense of A. Cs\'{a}sz\'{a}r [1]) on the set $X$. In this paper, we look into $\mathscr{G}$-continuous maps, $\mathscr{G}$-open and $\mathscr{G}$-closed maps, as well as $\mathscr{G}$-homoemorphisms in terms of $n$-GT spaces and establish some of their basic properties and relationships. Moreover, these notions are also examined with respect to the component generalized topologies of the underlying spaces by defining and characterizing pairwise versions of the said types of mappings.

A Generalized Topology from the Edge Set of Maximal Paths of Directed Graphs

“…Furthermore, Balingit C. and Benitez J. [9] in 2019 on their study on sets, functions and separation axioms in n-generalized topological space, introduced a particular example constructing an n-GT space (E(D), GE) defining GE = {v1, ..., vn} where vi = P(Ei) with Ei as the collection the edge set of the nontrivial maximal paths on a directed graph D, for i = 1, 2, ..., n.…”