Talk:Neighbourhood (mathematics)

message: I have mixed feelings about the recent changes to this article. It looks to me that the text is unnecessarily complicated, and the part contained in the ==Definition== section is no definition at all, rather some generalities, which I am having trouble following. Then, the way the article is now, one starts with the euclidean space, only to go to the topological space, then followed by a metric space, then back to the real numbers. 
Is there any way to integrate the recently inserted material? Oleg Alexandrov 02:44, 28 July 2005 (UTC)
thread_title:  Issues with recent additions to this article (request for comment) 

message: I second that.
This "wiggle" or "move" definition is pretty shit.
It's necessary a great deal of competence in making abstract mathematical concepts intuitive. In some cases it can rather make it even harder to comprehend. ?The preceding unsigned comment was added by 200.164.220.194 (talk) 23:33, 6 March 2007 (UTC)
replies: text: I changed "wiggle" to "perturb".  It sounds more formal, but I am not sure it is better... Best, Sam nead 17:31, 29 May 2007 (UTC)
thread_title:  'wiggle' or 'move' 2 

message: Oleg -- Those pictures are very cool!  Thank you for adding them -- they really help the article!  Question: how did you draw them?  Request: could you add a similar picture to the tubular neighborhood page?  This could be something as simple as a graph of a function in the plane, with a (green) shaded region around it.  (I like green!) Best, Sam nead 05:39, 30 May 2007 (UTC)
replies: text: I used Inkscape, it is free on both Windows and Linux. I could draw the picture you want, but perhaps you want to give it a try to take the picture I made as a base and modify it to do what you want, that way you may learn something new. :) Oleg Alexandrov (talk) 05:42, 30 May 2007 (UTC)
replies: text: Fair enough.  I'll take a look.  Best, Sam nead 15:04, 30 May 2007 (UTC)
thread_title: Pictures

message: The page Dehn twist refers to a 'regular neighborhood', which is also in the 'see also' sec'n of this article, but I cannot find a reference.  Is it the same as 'Uniform neighborhood'? If not, can we add a section to this article explaining what 'regular neighborhood' is and delete the 'see also' (unless reg. neighborhood is a vast and interesting topic deserving of its own article). Thanks. Zero sharp 15:07, 19 July 2007 (UTC)
replies: text: I think in this case it means symmetric around c.--Cronholm144 15:36, 19 July 2007 (UTC)

text: Regular neighborhood is indeed a big topic needing its own article.  There are even "relative regular neighborhoods", which should be considered a "power steering" version of the vanilla regular neighborhood.  To explain regular neighborhood, one would first need to specify a category (such as PL or DIFF) and then explain something like collapsing or whatnot.  On the other hand, all that is meant in the Dehn twist article is taking a closed annulus containing the curve as its core.  --C S 16:43, 13 September 2007 (UTC)
thread_title: Regular neighborhood

message: Under the subsection Neighbourhood of a point these paragraphs appear:
"If X is a topological space and p is a point in X, a neighbourhood of p is a subset V of X that includes an open set U containing p,
:p \in U \subseteq V."
This is also equivalent to p\in X being in the interior of V."
No, a definition is not equivalent to a statement; it's just a definition.50.205.142.50 (talk) 15:46, 12 June 2020 (UTC)
replies: text: It is not a definition, because the boundary of U might not be all of V. 67.198.37.16 (talk) 18:57, 26 November 2023 (UTC)
thread_title:  Fundamental misconception 

message: This passage from the intro is obtuse to the point it's almost unintelligible:
"Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount in any direction away from that point without leaving the set."
The word "point" is used 4 times with effectively no context. It's useless to someone who is trying to learn more about the article. It's probably useless to someone who already has a deep understanding of the article. Is it correct? I don't know, but I'm certain it's pedantic. 
My point is that the point of whoever wrote this fails to point out whatever point it is that they are trying to make. Can't someone do better? 69.63.125.25 (talk) 22:14, 1 March 2024 (UTC)
thread_title:  Intuitively speaking?