Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I can't image this, Someone can give a clear illustration?

share|improve this question

closed as not a real question by Harry Gindi, Joel David Hamkins, Ryan Budney, José Figueroa-O'Farrill, Theo Johnson-Freyd Mar 9 '10 at 3:43

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

2  
This question seems too localized. –  Harry Gindi Mar 9 '10 at 0:29
3  
Ken Baker has put up some beautiful images here: sketchesoftopology.wordpress.com/2010/03/25/bings-house –  j.c. Mar 31 '10 at 3:03
    
An update to jc's comment above: Ken Baker made a subsequent post that describes a deformation retraction: sketchesoftopology.wordpress.com/2010/06/23/… –  Ramsay Apr 9 '12 at 11:13

1 Answer 1

This is covered in Chapter 0 (the introductory chapter) of Algebraic Topology by Allen Hatcher.

share|improve this answer
2  
Yes, but is not clearly for me. –  gylns Mar 9 '10 at 0:28
3  
Hatcher gives a pretty lucid description. What part of it is not clear? He suggests visualizing a thickening of the space as made out of clay: have you tried using playdough? I have resorted to playdough many times when my visual imagination failed me. –  Steven Gubkin Mar 9 '10 at 0:35
4  
It sounds like this is a language issue. Imagine a drinking glass full of wax. It's a solid object. By melting the wax and draining the liquid wax, you in effect "hollow out the chamber" -- the chamber being the glass full of wax. The hollow chamber is the empty glass. –  Ryan Budney Mar 9 '10 at 1:04
2  
You can realize the deformation-retraction as a sequence (concatenation) of "elementary collapse" operations. In particular you can write the map as a piecewise construction, made of composites of rational polynomial functions. These elementary collapses appear in many places in Hatcher's book -- the main construction in Proposition 0.16 of Chapter 0 (page 15) is the first such explicit construction, I think. –  Ryan Budney Mar 10 '10 at 5:43
4  
You might want to take a look at Marshall Cohen's book "A Course in Simple Homotopy Theory". He's quite explicit about these sorts of details. –  Ryan Budney Mar 10 '10 at 6:28

Not the answer you're looking for? Browse other questions tagged or ask your own question.