Re: Regular topological spaces

William Elliot wrote:

From: Butch Malahide <fred.galvin@xxxxxxxxx>
Newsgroups: sci.math
Subject: Re: Regular topological spaces




let X be an infinite set, choose a point p in X, and call a subset
of X open if it has a finite complement or it does not contain p.



Isn't this space regular,


I think William is correct here. Consider the several cases for x and closed C, i.e., x = p or not, C containing p or not.

nay even Tychonov, as it's zero-dimensional?
In fact, it's a completely (even monotonically) normal T1 filter space.


BTW, I just noticed that Butch Malahide = Fred Galvin. I was wondering whatever happend to you, Fred. Good to see you are still here! I always value your posts.

--
Stephen J. Herschkorn                        sjherschko@xxxxxxxxxxxx
Math Tutor in Central New Jersey and Manhattan
.