proposed change of default name for P149

[StevenClontz]

I propose we change "$\varepsilon$-space" to "$\omega$-Lindelof". This aligns elsewhere on $\pi$-Base where we use $\omega$ to mean covering properties closed under finite powers, which is typically equivalent to the use of $\omega$ covers rather than open covers.

But I failed to find this usage in the literature. Maybe @ccaruvana has an idea?

[prabau]

Leaving the review to @ccaruvana. But here are two references using the name $\omega$-Lindelof:

https://zbmath.org/1153.54009 https://zbmath.org/0887.04001

and one using the name $\varepsilon$-space:

https://zbmath.org/1297.54047

(Gerlits & Nagy introduced the concept without giving it a name, except that it happened to be fifth one in a list of properties labeled by Greek letters $(\alpha)$, $(\beta)$, etc., which explains the later choice of name.)

[StevenClontz]

Gerlits & Nagy introduced the concept without giving it a name, except that it happened to be fifth one in a list of properties labeled by Greek letters

Another arugment for change - while "Lindelof" isn't exactly a semantic name for the covering property it describes, it's quite well known, and $\omega$-Lindelof makes the connection much clearer than $\varepsilon$-space.

[prabau]

Your argument makes perfect sense to me. @ccaruvana?

And apart from that, I think it would be good to list at least some reference for each of the names. And maybe explain where the name $\varepsilon$-space comes from?

[ccaruvana]

Thanks for the patience on this.