Generalized π -weak closed sets and some applications on weak structures

This article highlights the concept of generalized π -weak closed sets (briefly, gπ ( w ) -closed) in weak structures, that possess a lot of applications in information systems. We study their master properties and show the interrelationships between them and some types of sets with the help of counterexamples. Then, we applied gπ ( w ) -closed sets to define new types of the concepts of separation axioms, continuous functions, closed w -graph and strongly closed w -graph. We give some characterizations of these concepts and discuss main features. Moreover, we provide some examples to show some topological properties of these concepts that are losing in the frame of weak structures