I am currently confused by the following situation:
1) The metric $k$-center problem is inapproximable in polynomial time within $2-\epsilon$ unless $P=NP$.
2) The metric $k$-center problem can approximated within $1+\epsilon$ in time $O(k^{O(k/ \epsilon)})$
Did I just win a million dollars or why isn't this a contradiction? I guess my confusion comes from the unprecise statement "in polynomial time" in 1).