Let $X,Y$ be topological spaces and $f:X \rightarrow Y$
If $Y$ is compact and $G(f)$ (graph of $f$) is closed, show that $f$ is continuous.
I consider an open set in $X$, and as $G(f)$ is closed, $(X \times Y)-G(f)$ is open. And I guess I need to do something here. Then I can get some open sets. Also, I notice that compact is something relate to "finite". I guess I can use the compactness to do finite intersection or union and get the result finally.
But what should I do in the middle or I am not even on a right track.