Semi-stratifiable spaces and the insertion of semi-continuous functions (Q864704)

The autors give characterizations of perfect spaces, semi-stratifiable spaces and K-semi-stratifiable spaces in the sense of G.D. Creede in terms of mappings \(\phi: LSC(X)\to USC(X),\;UKL(X)\) with the corresponding properties, where \(LSC(X),\;USC(X)\) denote the set of all real valued semi-continuous, upper semi-continuous mappings, respectively, from \(X\) to \([0,1]\), and \(UKL(X)\) the set of all real-valued upper and K-lower semi-continuous functions from \(X\) to \([0,1]\).