I wanted to prove that if $C$ is a club (in a $\kappa$ cardinal) and $C\subseteq C'$ then $C'$ is also a club (that is if $C$ is of "mesure" $1$ then $C'$ is too). It is easy to see that $C'$ is unbounded. But I have some problems proving the closeness of $C'$. So, I try to find a $C'$ that is not a club!
Could somebody help me? thanks.