On lower and upper semi-continuous functions (Q2300108)

The authors study semi-continuous functions and Baire spaces in the context of generalized topological spaces. In particular, they give conditions which guarantee that a real-valued semi-continuous function is cliquish. (If \(\lambda\) and \(\mu\) are generalized topologies on a set \(X\), a real-valued function \(f\) on \(X\) is called \((\lambda, \mu)\)-cliquish if the set of all points in which \(f\) is \(\mu\)-continuous, is \(\lambda\)-dense.)