|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
Merging with topological manifold
I disagree with the merger. This article needs an expansion instead.
- 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)
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)