I was actually also planning to update that description. So we may take the opportunity to modify a few other things.
Removed the easy label, as some discussion may be needed.

@felixpernegger @yhx-12243 @Moniker1998
Here are a few suggestions to be discussed. Would like to solicit your opinion.

• change the name of the space to Stone-Čech compactification $\beta\omega$ of the integers
  i.e., add the symbolic name of the space as part of the pi-base name

• Should we use $\beta\mathbb N$ or $\beta\omega$ for the main symbolic name?

• Have $\beta\mathbb N$ as alias and remove all the other aliases

I'm not concerned. This is something @prabau will be good to decide on.

@felixpernegger @yhx-12243 @Moniker1998
Here are a few suggestions to be discussed. Would like to solicit your opinion.

• change the name of the space to Stone-Čech compactification $\beta\omega$ of the integers
  i.e., add the symbolic name of the space as part of the pi-base name

• Should we use $\beta\mathbb N$ or $\beta\omega$ for the main symbolic name?

• Have $\beta\mathbb N$ as alias and remove all the other aliases

Probably using $\beta\omega$ is more consistent, but as far as I see $\beta\mathbb{N}$ is the only one that is being used in the literature, so I would be inclined to keep that and maybe even renane to Stone Cech compactification of the natural numbers?
But I suppose either way is fine. We should really have the Čech instead of Cech though :)

but as far as I see $β \mathbb N$ is the only one that is being used in the literature

Maybe you haven't seen too much literature since $\beta\omega$ is certainly used just as often by specialists.

ok my bad

@felixpernegger should I make a commit with my suggestions above?

Yes your suggestions seem nice