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

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 This question seems too localized. – Harry Gindi Mar 9 2010 at 0:29
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 Ken Baker has put up some beautiful images here: sketchesoftopology.wordpress.com/2010/03/25/… – jc Mar 31 2010 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 2012 at 11:13

closed as not a real question by Harry Gindi, Joel David Hamkins, Ryan Budney, José Figueroa-O'Farrill, Theo Johnson-Freyd Mar 9 2010 at 3:43

1 Answer

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

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 Yes, but is not clearly for me. – gylns Mar 9 2010 at 0:28
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 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 2010 at 0:35
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 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 2010 at 1:04
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 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 2010 at 5:43
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 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 2010 at 6:28
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