8
$\begingroup$

It is known that in general convergence by sequences is not enough to account for all points in $\beta X \setminus X$, where $\beta X$ refers to the Stone-Cech compactification of a topological space $X$, and ultrafilters are needed. In fact, if $X$ is completely regular and Hausdorff, there are lots of points in $\beta X$ which are not the limits in $\beta X$ of any discrete subset of $X$ and these are called the "remote points" of $\beta X$. My question is, is it known whether the set of remote points in $\beta X$ is $F_\sigma$? Or are there known sufficient conditions on $X$ such that the set of remote points become $F_\sigma$? Thanks.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.