Generalized quotient topologies and hereditary classes

Abstract

We introduce a definition of $${\pi}$$ being injective with respect to a generalized topology and a hereditary class where $${\pi}$$ is a generalized quotient map between generalized topological spaces. This definition is mainly a sufficient condition to show several relations about a generalized topology and its induced generalized quotient topology when either is extended by a hereditary class or it can be regarded as an extension of a generalized topology via a hereditary class.