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Homework Statement
For some reason this one is really troubling me. So, a small hint (if possible) would be highly appreciated.
Let X be completely regular, and let A and B be disjoint closed subsets of X. If A is compact, there exists a continuous function f : X --> [0, 1] such that f(A) = {0} and f(B) = {1}.
The Attempt at a Solution
I've tried to solve this in different ways, but I don't seem to be getting anywhere. I don't see how compactness helps here - there's either something really obvious I'm missing here or a dubious result from one of the previous exercises which should be used here.