Extensions of semi-continuous functions (Q1346451)

This paper examines conditions under which a real-valued semi-continuous function \(f\), whose domain \(D\) is a subset of a topological space \(X\), can be extended to a real-valued semi-continuous function with domain \(X\). In general no separation axioms are assumed for \(X\). Special situations given particular attention are the cases where \(D\) is dense in \(X\), where \(D\) is closed in \(X\), where \(D\) is regular closed in \(X\), and where \(X\) is a linearly ordered space.