Let $\displaystyle (X,d_{x})$ be a continuous function. Suppose that $\displaystyle K\subset X$ is compact and that $\displaystyle A\subset\ \mathbb{R}^k$ is compact.

Prove that $\displaystyle f(K)\bigcap A\ =\ \emptyset$ implies dist$\displaystyle (f(K),A)>0$

It's analysis and there isn't an extra class for that unlike the other modules (even though it's considered the hardest).

Thnx in advance