This article has not yet been rated on Wikipedia's content assessment scale. |
I haven't read the definition of local homeomorphism anywhere, but I would disagree with the definition given in the article: the first-coordinate inclusion R→R2 does not feel like a local homeomorphism to me.
Also, for a covering map one needs a bit more than just a surjective local homeomorphism. AxelBoldt 05:55 21 Jun 2003 (UTC)
You are certainly right. I rewrote the article: I think it looks a bit better now. Note that a surjective local homeomorphism between compact Hausdorff spaces is always a covering map but the converse fails, of course. -- PS T 20:58, 18 January 2009 (UTC)
"Every homeomorphism is of course also a local homeomorphism, but this is boring." This is poorly worded: 1) The coordinating conjunction "but" sets up a contradiction/negation of a previous idea, but the follow "this is boring" is either a positive addition to the point or a logical continuation (usually "and" or "so," respectively); and 2) "of course" and "boring" are hardly professional and only add to the verboseness of the statement. A better way to word this statement would be: "By definition, every homeomorphism is a local homeomorphism." This is clear and to the point and informs the reader of the fact at hand without extraneous language. — Preceding unsigned comment added by 97.94.204.72 ( talk) 17:34, 17 March 2013 (UTC)
In the "Formal Definition" the open set U gets silently promoted to a topological space - one should mention that the subspace topology is assumed, which might not be obvious to someone approaching the definition for the first time.
This article has not yet been rated on Wikipedia's content assessment scale. |
I haven't read the definition of local homeomorphism anywhere, but I would disagree with the definition given in the article: the first-coordinate inclusion R→R2 does not feel like a local homeomorphism to me.
Also, for a covering map one needs a bit more than just a surjective local homeomorphism. AxelBoldt 05:55 21 Jun 2003 (UTC)
You are certainly right. I rewrote the article: I think it looks a bit better now. Note that a surjective local homeomorphism between compact Hausdorff spaces is always a covering map but the converse fails, of course. -- PS T 20:58, 18 January 2009 (UTC)
"Every homeomorphism is of course also a local homeomorphism, but this is boring." This is poorly worded: 1) The coordinating conjunction "but" sets up a contradiction/negation of a previous idea, but the follow "this is boring" is either a positive addition to the point or a logical continuation (usually "and" or "so," respectively); and 2) "of course" and "boring" are hardly professional and only add to the verboseness of the statement. A better way to word this statement would be: "By definition, every homeomorphism is a local homeomorphism." This is clear and to the point and informs the reader of the fact at hand without extraneous language. — Preceding unsigned comment added by 97.94.204.72 ( talk) 17:34, 17 March 2013 (UTC)
In the "Formal Definition" the open set U gets silently promoted to a topological space - one should mention that the subspace topology is assumed, which might not be obvious to someone approaching the definition for the first time.