I'm studying the ordinal space $[0,\kappa[$ where $\kappa\neq \omega$ is a cardinal of countable cofinality and I want to know why there are in $[0,\kappa[$ two disjoint closed sets of cardinality $\kappa$.

The case when $\kappa=\omega$ it's obvious but I can't prove the general one... If anybody could help me I would be more than gratefull.

Thanks!

countable cofinality. $\endgroup$ – Włodzimierz Holsztyński Jan 5 '15 at 10:07cardinalitytoo. I had overlooked everything! $\endgroup$ – Włodzimierz Holsztyński Jan 5 '15 at 10:12