Given a topological space $X$ and a compactification $\alpha X$ of it, I want to refer to the points of $\alpha X-X$. Here is my problem: Since I want to do this in an abstract, and since here I always write 'foo compactification' instead of $\alpha X$, I would like to refer to the points of $\alpha X-X$ via a simple phrase or just a word, e.g. 'compactification points' or 'points at infinity'. Now 'compactification points' can easily be misunderstood to mean the points of $\alpha X$, whereas 'points at infinity' sounds a bit sloppy.
In Engelking's and Willard's books on topology I did not find a name for the points of $\alpha X-X$, and my online research kept showing me general questions about the one-point and the Stone-Cech compactification.
Do you know a name/really short phrase for the points of $\alpha X-X$ that is accepted in the field, or can you say that there is no commonly known such name?
If there is no such name, of course I can work around it by naming the 'foo compactification', but being unable to find an answer to this simple question by myself made me curious.
Thank you!
It's standardly called "the remainder". For the particular case of the Cech-Stone compactification $X^\ast$ is used for $\beta X\setminus X$. So just say the remainder of $X$ to refer to the new points. Point(s) at infinity is used for the one-point compactification, or the (linear) two-point compactification.