The closed graph theorem as given in my notes, reads:
Let $f_1, f_2:(X, \tau) \mapsto (Y, \tau')$ be continuous functions between topological spaces. If $\tau' $ is Hausdorff,then $\Gamma =\{p \in X | f_1(p)=f_2(p)\} \in \tau^*$ ($\Gamma$ is a closed set).
My question is: What is the intuition behind this theorem and the reason for the name? I see no graph here, I mean $\Gamma$ is not even a graph, is just a subset of $X$ so where this "closed graph" and why is it called closed. Besides we have two functions here, I haven't been able to find this definition using two functions anywhere else as they do in my notes
Wikipedia's article seems to imply closed graphs are just the graphs of of continuous functions.