Talk:Retraction (topology)

message: Hmmmm...
"a continuous map r is a retract if ... In this case, A is called a retract of X, and r is called a retraction"
make up your mind, dudes
:Fixed. Apart from the repetition, the map is called a retraction, while the subspace is a retract. There was some confusion about it. Alvisetrevi 10:25, 27 September 2007 (UTC)
thread_title: Untitled

message: I've seen the phrase "strong deformation retract".  How's that related to "deformation retract"?  thanks!  --345Kai 16:10, 5 March 2007 (UTC)
thread_title:  strong deformation retract? 

message: "However, there exist contractible spaces which do not strongly deformation retract to a point."
An example of this here would be fantastic. msgj 09:18, 11 October 2007 (UTC)
replies: text: A space that deformation retracts to a point is contractible, however the converse is not true. For example, see Hatcher's book: Chapter 0, Exercise 6(b) (an explanation/solution can be found here. It is important to note that the dense subset of rational numbers inherits its subspace topology from \mathbb{R}). And when we say "deformation retracts to a point", there is no distinction between strong and weak deformation retracts. Hence, I am changing the second statement under the "properties" section to it's original (see this diff). -  Subh83 (talk | contribs) 23:43, 30 November 2011 (UTC)
replies: text: Of course the distinction between deformation retract and strong deformation retract should be made in the sentence you reference, because this article distinguishes the notions.  You are citing Hatcher to support removal of the word "strongly", but as explicitly pointed out earlier in the article, his notion of deformation retract is a strong deformation retract in the sense of this article.  The sentence without the word "strongly" would be fine if it were written inside of Hatcher's book, but it is not.  It is written in the context of this article.128.196.226.219 (talk) 21:09, 25 January 2013 (UTC)
thread_title:  Example? 

message: How is a retraction different from an idempotent map on X? If r: X \rightarrow A is a retraction then  r(r(x)) = r(x)  because r(x) \in A. OTOH, if r is idempotent then for all a in the codomain of r there's some x such that r(x)=a therefore r(a)=r(r(x))=r(x)=a. The two definitions seem therefore equivalent, yet the respective articles don't even mention each other.  —Preceding unsigned comment added by 192.114.107.4 (talk) 07:54, 16 September 2008 (UTC)
replies: text: Well, what you say would be true only if your idempotent map was 1) surjective 2) continuous. Indeed, you're stating "for all a in the codomain of r there's some x such that r(x)=a". But what if not all the elements of A lie in the codomain of r?. A practical example: the absolute value from complex numbers to real numbers. It is idempotent, but definitely not a retraction (e.g. r(-5)=5 \neq -5 ). Alvisetrevi (talk) 21:37, 10 October 2008 (UTC)
thread_title:  Retraction v/s Idempotency 

message: Since when do we give attributions and licensing information on a wikipedia page?  Either the info we put is free, or if it isn't and needs attribution, it shouldn't be used.--24.85.90.31 (talk) 02:35, 30 November 2011 (UTC)
thread_title:  attributing sources 

message: Hello,
I stumbled across this article and was a little confused. Apparently, retract redirects here. It seems to me that retract is the more general topic and deformation retract should be a redirect. This is mainly because Munkres (and this article) presents retraction first and then uses it to define deformation retraction. Any thoughts? Happy Squirrel (talk) 16:06, 2 December 2015 (UTC)
replies: text: Since there were no objections, I have performed the move. Happy Squirrel (talk) 22:34, 8 December 2015 (UTC)
thread_title:  Proposing a move to [[Retract]] 

message: Substituted at 18:34, 17 July 2016 (UTC)
thread_title: Assessment comment

message: The introductory paragraph contains this passage:
"An absolute neighborhood retract (ANR) is a particularly well-behaved type of topological space. For example, every topological manifold is an ANR. Every ANR has the homotopy type of a very simple topological space, a CW complex."
This is an extremely bad place to put this passage.
The passage is also completely stupid.  Yes: completely stupid.  Why? The passage introduces a new concept (ANR) without defining it.  
But despite not defining it, it gives information about it ("For example, every topological manifold is an ANR. Every ANR has the homotopy type of a very simple topological space, a CW complex").
Nothing could be more of a WASTE of Wikipedia space and a waste of readers' time.
Do not discuss technical information about some undefined concept!!!  And above all, never do this in the introductory paragraph of an article whose subject is a math concept *not the same as* the other concept intruding on the subject of the article.
Note: It is obviously a good idea to mention ANR's in the article. But 1) When they are mentioned, they should be defined, and 2) The placement of this text should be well down in the article, AFTER the subject of the article (retracts in topology) is discussed and defined.2600:1700:E1C0:F340:4E1:BA76:7792:7B25 (talk) 19:07, 18 February 2019 (UTC)
thread_title:  Very bad placement