On decompositions of continuity in topological spaces (Q624252)

By using \(m\)-structures \(m_{1}, m_{2}\) on a topological space \((X, \tau)\), the authors define a set \(D(m_{1}, m_{2})=\{A: m_{1}\text{Int}(A) = m_{2}\text{Int}(A)\}\), where \(m_1\) and \(m_2\) are minimal structures on a nonempty set \(X\), and obtain many decompositions of open sets and weak forms of open sets. Thus the decompositions provide many decompositions of continuity and weak forms of continuity.