Some generalized continuous functions and resolvable and irresolvable spaces (Q1386819)

A topological space \(X\) is called resolvable if it is the union of two disjoint dense subsets, otherwise it is called irresolvable. The main results in this paper are: 1) A space \(Y\) is irresolvable if and only if for every space \(X\) , every weakly somewhat open function \(f: X\rightarrow Y\) is somewhat open; 2) A space \(Y\) is resolvable if and only if for every space \(X\), every \(R\)-continuous function \(f: X\rightarrow Y\) is continuous.