# Hausdorff space

## Primary tabs

Defines:
Hausdorff, Hausdorff topology, T2, T2 topology, T2 axiom
Synonym:
Hausdorff topological space, T2 space
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### metric space

perhaps mention that metric spaces are a common example of hausdorff spaces?

### correction not message!

This should be a correction (others take note too!). As a message it is impossible to "resolve" your comment.

Note that there is an "addendum" correction type, so you are free to suggest whatever you'd like to any entry.

apk

### about the entry called "Hausdorff"

I have actually the following proposal. There is an entry in encyclopedia called "Hausdorff". Since this entry is just linked to a T2 space, I think it reasonable to rename it to "Hausdorff space".

If you type in the Google the following searchs, you'll get the corresponding amount of links, which can be seen as some indication of how frequently they are used:

"T2 space" - 567
"Hausdorff topological space" - 1.710
"Hausdorff space" - 11.600

So, imagine someone find the notion "Hausdorff space" in some article. He goes to PlanetMath, and find no entry for "Hausdorff space". Of cource if he is determined enough, he could look through every entry with the name Hausdorff and finally finds what he needs, but it is better to have a direct link with name "Hausdorff space".

### Re: about the entry called "Hausdorff"

In some far distant future PM will hopefully
have a mathematical front page. A very primitive
version is here:

http://planetmath.org/?op=getobj&from=objects&name=OverviewOfTheContentO...

Once everything is in place, I think it will be
much more easier to find things at PM. Searching
for a mathematical concept is very difficult.

### Re: about the entry called "Hausdorff"

There is no need to rename entries. In order to have "Hausdorff space" appear is to add the terms "Hausdorff space" and "Hausdorff topological space" to the "also defines" list of the entry on T_2 spaces. Also, "Hausdorff" should definitely remain on the "also defines list since otherwise the linker won't pick up on stuff like "If $X$ is also Hausdorff, then a stronger form of this theorem apples." There is no problem with having both "Hausdorff" and "Hausdorff space" on the "also defines" list since the linker picks the longest match.

### Re: Re: about the entry called "Hausdorff"

Ok, I completely agree with it. That is what I actually made as a correction to the entry "T2 space", but it was rejected, perhaps because of nonclearly formulated goal. Now I hope it is more clear :)

### Re: about the entry called "Hausdorff"

Would putting "Hausdorff" in Keywords Section serve the same purpose?

### Re: about the entry called "Hausdorff"

First of all, I don't see any Keywords Section. But even if such section would exist, putting "Hausdorff" there, won't help a poor man to find out what is "Hausdorf space".

### Re: about the entry called "Hausdorff"

it would (it'd improve the entry ranked in the search engine)

But again, I don't wee what's the big fuss.
Entries can have SEVERAL titles, that's what the "synonyms" filed are on the editing page.

And mine has both T2 and Hausdorff
and searching both for T2 space and Hausdorff Space will hit mine
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

### Re: about the entry called "Hausdorff"

> I don't wee what's the big fuss.
> searching both for T2 space and Hausdorff Space
> will hit mine

Well that's true, the only point is that searching engine doesn't work for the moment on PlanetMath (in fact, as far as I aware it doesn't work for a quite long time). One can make a Google query "Hausdorff space" of the PlanetMath, and than the first thing which will come up will be your entry. Anyway, as I see you already made an entry "Hausdorff Space" ;), and "that is good so" ;)