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Homework Statement
Let (X,\tau_X) and (Y,\tau_Y) be topological spaces, and let f : X \to Y be continuous. Let Y be Hausdorff, and prove that the graph of f i.e. \graph(f) := \{ (x,f(x)) | x \in X \} is a closed subset of X \times Y.
Homework Equations
The Attempt at a Solution
Which property of closed set should I use to prove this? Should I assume a sequence inside the graph set converging to some (x,y) \in X and then somehow show that this limit point belongs to the graph? Or should I prove that the complement of the graph set is not open? I don't know how to finish the proof with either approach. Please give me some hint.