Expansion of open sets and decomposition of continuous mappings (Q1891455)

For a topological space \((X, \tau)\) a mapping \(\Phi: X\to 2^ X\) is called an expansion on \(X\) if \(U\subseteq \Phi(U)\) for each \(U\in \tau\). Using this concept the author defines \(\Phi\)-expansion continuous mappings between topological spaces which enables him to provide a very general decomposition of continuity. As a corollary he obtains the well known result that a mapping between two topological spaces is continuous if and only if it is weakly continuous and weak* continuous.