Talk:Non-Hausdorff manifold

The term "Prüfer manifold" (or "Prüfer surface") is unambiguous[edit]

The article states (under the section Prüfer surface):

"Gabard . . . discusses the Prüfer surface (actually 2 related manifolds, both called by this name), as a 2-dimensional example."

The parenthetical phrase is true in the referred-to paper — by Gabard — but it is not true in general.

Although Gabard uses the term "Prüfer surface" to refer to the Calabi-Rosenlicht surface (a related but not identical construction), this is not at all common in mathematics. The phrasing should be modified to reflect this fact.

Even Gabard points out in the first footnote:

"Actually, the surface we consider is not exactly the original Prüfer surface, but rather Calabi-Rosenlicht’s slight modification of it."

Although he calles the modification "slight", he mentions that the Prüfer surface is non-separable, whereas the Calabi-Rosenlicht surface is separable.

Gabard also states:

"We call it also the Prüfer surface (even though it seems to appear explicitly only in the paper by Calabi-Rosenlicht [2])."

And incidentally, the "Prüfer surface" is much more commonly called the "Prüfer manifold". I suggest that Wikipedia do the same.Daqu (talk) 17:48, 7 September 2008 (UTC)[reply]

Prüfer surface is Hausdorff?[edit]

Look at the article. Proposition 3.1 says that the surface is Hausdorff. This article should either have an explanation of what this thing is, or not reference it at all. In the short term, I have removed it. —Preceding unsigned comment added by 68.226.88.170 (talk) 18:28, 4 May 2010 (UTC)[reply]

Second example is Hausdorff non-manifold[edit]

I don't understand why the branching line is in this article, because it doesn't seem to be an example of a non-Hausdorff manifold. — Preceding unsigned comment added by 195.37.142.72 (talk) 17:15, 29 July 2016 (UTC)[reply]

It is a manifold because every point has a neighborhood homeomorphic to an open subset of the real line. It is non-Hausdorff because any neighborhoods N(0_a) and N(0_b) of the two origins 0_a = (0,a) and 0_b = (0,b), respectively, must intersect. 2601:200:C000:1A0:3932:3D49:97C7:A86A (talk) 17:47, 21 September 2021 (UTC)[reply]

"Non-Hausdorff" listed at Redirects for discussion[edit]

An editor has identified a potential problem with the redirect Non-Hausdorff and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 January 27#Non-Hausdorff until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Jay (talk) 17:21, 3 February 2022 (UTC)[reply]