Hausdorff and Closed Set equivalence This is a question I've been stuck on for a half hour, and I fear there is some elementary trick I may be missing. I have done the "commonly seen" direction, and cannot do the other:
Let $Y$ topological space. Show that $Y$ is Hausdorff iff for all topological spaces $X$, and pairs of continuous maps $f$,$g$ $:X \to Y$, the set {${x \in X : f(x) = g(x)}$} is closed.
I have shown that $Y$ Hausdorff implies that our set is closed easily. The other direction eludes me. Can anyone write maybe the first two-three lines of a successful solution? This is embarrassing!

Hint Can you find a suitable space $X$ and suitable functions for which $\{x\in X:f(x)=g(x)\}$ is $\{(y,y):y\in Y\}$?
