# Stationary and closed and unbounded sets.

• January 9th 2011, 12:29 PM
pavelr
Stationary and closed and unbounded sets.
Hi,

Having hard time solving the following:

1. Given $\kappa$ is a regular cardinal, for every $\lambda$< $\kappa$ we'll define E={ $\alpha$ < $\kappa$ | cf $\alpha$ = $\lambda$}. Prove that every such set is stationary.
2. f: $\kappa$ -> $\kappa$ . Prove that C = { $\alpha$ < $\kappa$ | f| $\alpha$: $\alpha$-> $\alpha$} is closed and unbounded.

Sorry for the mess, I have never used TEX before.

Thanks in advance, every help will be appreciated.