1. The problem statement, all variables and given/known data Let K be a compact sebset of a metric space (X, d) and let [itex]\epsilon[/itex] greater than 0. Prove that there exists finitely many points [itex]x_1 x_2, ... x_n \in K[/itex] such that K is a subset of the union of the [itex]\epsilon[/itex] neighborhoods about [itex]x_i[/itex] 2. Relevant equations N/A 3. The attempt at a solution I think all I need to show is that all of the neighborhood epsilon disks about all the x's cover K and since K is is a compact set then finitely many of these neighborhoods cover K. If that is the correct approach then I'm just not sure how to start it. We didn't do any examples of proving that a certain set covers another.