gm-continuity on generalized topology and minimal structure spaces

Abstract

We introduce the concepts of gm-continuity, GM-converge to a point on generalized topology and minimal structure spaces. Also, we introduce the notions of gm-T 2 space, gm-closed graph and strongly gm-closed graph on generalized topology and minimal structure spaces. We obtain several characterizations and properties of gm-continuous functions by using the interior operator and closure operator defined on both a generalized topology g and a minimal structure m. Moreover, we investigate some properties for gm-continuous functions by using the notions of gm-T 2 space, gm-closed graph and strongly gm-closed graph.

On mω ̂-light functions

“…̂-open sets we provided ̂-disconnected and ̂-totally disconnected spaces, and illustrate the relation between them. Definition (1.1) [5]: Let be a non-empty set, a sub collection of the power set ( ) is called -structure if it contains ∅ and , the pair ( , ) is called -structure space (briefly -space). Any elements in is said to be -open set, is said to be closed.…”

Operational properties involving functions with generalized continuity

“…Császár in 2002 introduced the notion of generalized topology in [2], which differs from the notion of topology for lacking the property about finite intersection of open sets. From this notion many types of generalized continuity can be defined in these generalized topological spaces, for example, (g, g ′ )continuity [2], θ(g, g ′ )-continuity [2] and gm-continuity [12]. In the year 2000, Popa and Noiri introduced in [10] the concept of minimal structure and from that concept they introduced a version of generalized continuity called m-continuous functions [9,10].…”

Preopen sets and prelocally closed sets in generalised topology and minimal structure spaces

“…In 2013, Zakari [11] studied on some generalisations for closed sets in generalised topology and minimal structure spaces. He also studied gmcontinuous functions between GTMS spaces in [12]. The idea of a locally closed set in topological space was defined by Kuratowski and Sierpinski [6].…”