Unified theory of the kernel of a set via hereditary classes and generalized topologies

We build a unification of several variants of the kernel of a set in a generalized topological space endowed with a hereditary class, which is a fundamental concept to introduce new modifications of important concepts as open sets and closed sets. This new theoretical framework leads to the study in unified form of separation properties in a context much more general and versatile than the case of a topological space provided with an ideal.