Talk:Normal space
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[edit]I changed T4 back to "normal Hausdorff", since I prefer self-explanatory unambiguous terminology. Everybody who sees the term "normal Hausdorff" knows what's going on, no matter when they learned topology. AxelBoldt
I removed this add-on to Tietze:
- (If X is normal regular, then we may be able to extend the function when A is not closed; see Extension by continuity.)
The Extension by continuity article requires the target Y to be regular, not the source X. AxelBoldt 19:41 Aug 30, 2002 (PDT)
You're right; it's because R is regular that such an extension may be possible. But in any case, it's really two separate issues; you use extension by continuity (in certain circumstances) to extend to the closure of A, then use the Tietze extension theorem (in any circumstance) to extend to X, and there's really no interaction between these. — Toby 12:38 Sep 4, 2002 (PDT)
PS: I'm looking to see where I got that Stone Cech illustration in Regular space, and how it plugs the gaps in the case when X is indeed the SC compactification. (Or if it was wrong anyway ^_^.) — Toby
T6
[edit]Are perfectly normal (Hausdorff) spaces also called T6? The taxobox certainly implies so; I haven't seen this, but it would make perfect sense. If so, then this fact should be added to Separation axiom and (at the very least!) here. —Toby Bartels 09:32, 18 August 2006 (UTC)
Even I was wondering, T6 redirects here but the page makes no mention of T6 anywhere. --Kprateek88(Talk | Contribs) 16:42, 2 November 2006 (UTC)
- The Encyclopedia of General Topology (2004, ed. Hart, Nagata, and Vaughan) defines T6 spaces as perfectly normal Hausdorff spaces (p. 158). I'll add this terminology to the article since it fits in nicely with the other Ti axioms. -- Fropuff 19:09, 8 November 2007 (UTC)
- FWIW: Munkres also refers to perfectly normal Hausdorff spaces as T6. -- Fropuff 06:09, 10 November 2007 (UTC)
Very confusing first two sentences
[edit]The article begins as follows:
"In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space."
This seems to mention two distinct meanings for the term "T4 space".
They seem to imply, without ever addressing this clearly, that a normal space is not necessarily Hausdorff.
If this is right, it would be immensely helpful if the article made this emphatic rather than just casually mentioning it.
To make matters worse, "T4" is used later in the article, without its meaning having been clearly specified in the article.
I hope someone knowledgeable about this topic and also able to write clearly can fix this.
- You are right that this may be a little confusing. Axiom T4 is not the same as a T4 space; it's preferable to remove mention of it here. I'll also try to clarify a few other things. PatrickR2 (talk) 05:11, 22 May 2025 (UTC)
- Also, note that "T4 space" is clearly defined in the second paragraph of the Definitions section. PatrickR2 (talk) 05:33, 22 May 2025 (UTC)