On generalized $B^*$-continuity, $B^*$-coverings and $B^*$-separations

There are various generalizations of continuous functions in topological spaces and $B^*$-continuity is one of them which deals with the Baire property and denseness of the space. We have defined and discussed several properties and interrelations of some further generalizations of $B^*$-continuity, namely, contra $B^*$-continuity, slight $B^*$-continuity and weak $B^*$-continuity. We have also defined certain notions of generalized coverings and separations in terms of $B^*$-sets and studied the effect of generalized $B^*$-continuous functions on spaces having these covering and separation properties.