If $\kappa$ is a cardinal then a set $C\subseteq\kappa$ is closed iff for any $S\subseteq C$ and $\alpha<\kappa$ $\sup(S\cap \alpha)=\alpha$ then $\alpha\in C$ (That is, if the limit of some sequence in $C$ is less than $\kappa$ then the limit is also in $C$ )

If $\kappa$ is a cardinal and $C\subseteq\kappa$ then $C$ is unbounded if, for any $\alpha<\kappa$ there is some $\beta\in C$ such that $\alpha<\beta$

If a set is both closed and unbounded then it is a club set.