```Date: Jan 21, 2013 3:59 AM
Author: William Elliot
Subject: Re: G_delta

On Sun, 20 Jan 2013, Butch Malahide wrote:> On Jan 20, 12:14 am, William Elliot <ma...@panix.com> wrote:> >> > Your proof generaly follows the proof for f in 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.Ok, the other difference is a)	regular & every point a G_deltaandb)	every point the countable intersection of closed nhoods of the point.That is for all p, there's some closed Kj, j in N withfor all j in N, p in int Kj & {p} = /\_j Kj.Yes, a) -> b) but I doubt the converse.In other words, is a) strictly stonger than b).Now if we assume a Lindelof space, is a) still strictly stronger than b?I think it is.  Are you of the same opinion?
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