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 $$f \colon X \to Y$$ […]