New open set on topological space with generalized topology

Abstract

We all know the vast number of studies that presented several generalizations of open sets in topological spaces. On the other hand, since 2002 when A. Csaszar introduced the definition of generalized topology, other generalizations of open sets have appeared in generalized topological spaces. Our study provides a new generalization for an open set, where the definition will be a mixture of ordinary topology and generalized topology. Our new open set is named Xw-open set. We give several characterizations, properties, and examples related to the new concept.