
Re: G_delta
Posted:
Jan 14, 2013 1:04 AM


On Sun, 13 Jan 2013, Butch Malahide wrote: > On Jan 13, 11:09 pm, William Elliot <ma...@panix.com> wrote:
> > If p is a point in a compact Hausdorff space, is {p} a G_delta set? > Not necessarily. > > Example: [0, omega_1] with the order topology. {omega_1} is not a > G_delta set.
Oh of course, and that was the very space I was wrestling with.
> Example: The Tychonoff product of uncountably many 2point discrete > spaces. No singleton is a G_delta set.
In 1st countable spaces, every point p is G_delta. In fact, if every point of a compact Hausdorff space S, is G_delta, then S is 1st countable.
Define g:omega_1 > omega_1 + 1, eta > eta. Assume S is compact Hausdorff and f in C(omega_1, S).
Is there some h in C(omega_1 + 1, S) with f = hg?

