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 remote points become $F_\sigma$? Thanks.



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