Talk:Closed manifold

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Stub Class	Mid Priority	Field: Topology
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 18:57, 21 May 2007 (UTC)

[edit] Merging with topological manifold

I disagree with the merger. This article needs an expansion instead.

Besides, the article topological manifold is in a sorry state. Please ask again after it is improved. Oleg Alexandrov (talk) 23:45, 26 November 2005 (UTC)

And besides, I see no harm in putting some of this material at topological manifold while still keeping this separate and with more detail. Oleg Alexandrov (talk) 04:14, 22 December 2005 (UTC)

[edit] Definition wrong

In my opinion, a closed manifold is a manifold with each connected component compact, i.e. it is not open. Otherwise one would call it compact, there would be no need to introduce a new expression. Hottiger 10:57, 14 April 2006 (UTC)

Hottiger, I agree that the terminology is confusing. In common use, "compact manifold" means a compact manifold possibly with boundary, while closed means compact without boundary. This confused and bothered me at first too; the reason for the term (as I understand it) is that "compact manifold without boundary" and "compact manifold with boundary" are both common concepts, but the full terms are verbose, hence they are abbreviated to "closed manifold" and "compact manifold".

I've added clarification to the article; hope it helps.

Nbarth 20:06, 1 December 2007 (UTC)