
Re: G_delta
Posted:
Jan 20, 2013 3:35 AM


On Jan 20, 12:14 am, William Elliot <ma...@panix.com> wrote: > > Your proof generaly follows the proof for f in C(omega_0,S),
You mean C(omega_1,S).
> where S is regular Lindelof and ever point is G_delta, that > f is eventually constant. There are some differences in the > premises of the two theorems that I'm going to puzzle upon > and try to harmonize.
The puzzle is whether I needed to put that silly adverb "hereditarily" in front of "Lindelof". Now that you mention it, just plain Lindelof is good enough. I only used "hereditarily Lindelof" to show that Z is Lindelof. It's easy to see (as shown in the last step of the argument I posted) that Y\Z contains at most one point. It follows from the other assumptions that Y\Z is a G_{delta}, i.e., Z is an F_{sigma} in Y; and of course an F_{sigma} subspace of a Lindelof space is Lindelof.

