Problem:
Let X be a metric space and let be a sequentially compact subspace. Let p be a point in X\K. Prove that there is a point that is closet to p of all points in K in the sense that
for all points q in K.
Is this point unique?
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Suppose that is sequentially compact subspace of the metric space X. Then K is a closed subset of X.
Define the function by for all q in K and p be a point in X\K. I want to show that this function f is continuous first, but I don't know how nor what theorem to use.
Thank you for your time. Much appreciated.