If f is a continuous function from X to Y, the graph of f,
graph(f) = {x, y) : y = f (x), x ∊ X}
is a closed subset of X × Y.
The converse of this result is not true in general. The following exercise details a partial converse in the special case in which the range Y is compact. Later we show that converse also holds for linear functions (exercise 3.37), a fundamental result which is known as the closed graph theorem.