The topological closed graph theorem

There are a number of theorems in various settings that link continuity of a function \(f\colon X \to Y\) to closedness of that function’s graph – i.e., the set of all points \((x,y)\in X \times Y\) such that \(y = f(x)\). For example, we learn in functional analysis that if \(f \colon X \to Y\) […]