(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex](X,\tau_X)[/tex] and [tex](Y,\tau_Y)[/tex] be topological spaces, and let [tex]f : X \to Y[/tex] be continuous. Let [tex]Y[/tex] be Hausdorff, and prove that the graph of [tex]f[/tex] i.e. [tex]\graph(f) := \{ (x,f(x)) | x \in X \}[/tex] is a closed subset of [tex]X \times Y[/tex].

2. Relevant equations

3. 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 [tex](x,y) \in X[/tex] 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.

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# Homework Help: Product topology, closed subset, Hausdorff

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