Functions with a closed graph

Abstract

Let X X be a T 2 {T_2} Baire space. A set F ⊂ X F \subset X is closed and nowhere dense in X X if F F is the set of points of discontinuity of a function with a closed graph from X X into R n {R^n} . Although the converse does not hold in general, it does hold when X X is the real line.