Talk:Normal space

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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

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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

[edit] T₆

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 T_i 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)