4
$\begingroup$

Let $X=\beta\omega\setminus\omega$ and let $Y=X\setminus P$ where $P$ is the set of P-points in $X$. Then $P$ is dense in $X$ if we assume CH but $P$ may be empty otherwise (Shelah). In the one case $Y$ is nowhere locally compact and in the other case $Y$ is a compact Hausdorff space. Elsewhere I have asked whether spaces like $Y$ (i.e. compact Hausdorff spaces with their P-points removed) are Baire spaces. Here I would like to ask about other properties of $Y$.

For example, $Y$ is a completely regular Hausdorff space, come what may. Is $Y$ always normal? Is $Y$ always Lindelof/weakly Lindelof? Is the ring of bounded continuous functions on $Y$ independent of the set theory in which one is working (equivalently, does $X$ always equal $\beta Y$)?

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.