Stationary nonclosed member of the club filter
= Stationary nonclosed member of the club filter
{title2=$\kappa\setminus\{\omega\}$}
For any regular uncountable <cardinal number> $\kappa$, the set $\kappa\setminus\{\omega\}$ contains the final-segment <club set> $[\omega+1,\kappa)$, so belongs to the <club filter> and is a <stationary set>. It is not closed, since its finite ordinals have supremum $\omega$, which is missing.