Club filter
= Club filter
{title2=$\mathcal D_\kappa=\{A\subseteq\kappa:\exists\text{ club }C\subseteq A\}$}
On a regular uncountable <cardinal number> $\kappa$, the club filter consists of all subsets containing a <club set>. It is a <kappa-complete filter> by <club filter completeness>. Its members are <stationary sets>, although a <stationary set> need not be a filter member, and a filter member need not itself be closed.