Deformation retraction to a point is a stronger condition,so is there a example of a contractible space that does't deformation retract onto any point?
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Consider two dimensional sphere which can not be deformed into a point. – HK Lee Oct 20 '18 at 09:14
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You can find example of such space in Hatcher’s (Algebraic topology) exercise – Mayuresh L Oct 20 '18 at 09:18
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@HK Lee but why it's contractible? – Daniel Xu Oct 20 '18 at 09:25
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Sorry. I confused with a retraction. – HK Lee Oct 20 '18 at 09:26
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@HKLee. The sphere isn't contractible. – Oct 20 '18 at 09:27
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@MayureshL write an answer referring to the exact page of the example, e.g. – Henno Brandsma Oct 20 '18 at 09:57
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some googling reveiled this answer – Henno Brandsma Oct 20 '18 at 09:58
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Some relevant answers: https://math.stackexchange.com/questions/166648/why-does-the-zig-zag-comb-weakly-deformation-retract-onto-a-point https://math.stackexchange.com/questions/126342/why-doesnt-the-zig-zag-comb-deformation-retract-onto-a-point-even-though-it – Henno Brandsma Oct 20 '18 at 10:01
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@Henno Brandsma well,it's a nice example – Daniel Xu Oct 20 '18 at 10:03
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https://math.stackexchange.com/questions/2913383/x-is-contractible-if-and-only-if-there-exists-a-deformation-retract-to-a-point/2913423#2913423 – Andres Mejia Oct 21 '18 at 03:20