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?

  • $\begingroup$ Consider two dimensional sphere which can not be deformed into a point. $\endgroup$ – HK Lee Oct 20 '18 at 9:14
  • $\begingroup$ You can find example of such space in Hatcher’s (Algebraic topology) exercise $\endgroup$ – Mayuresh L Oct 20 '18 at 9:18
  • $\begingroup$ @HK Lee but why it's contractible? $\endgroup$ – Daniel Xu Oct 20 '18 at 9:25
  • $\begingroup$ Sorry. I confused with a retraction. $\endgroup$ – HK Lee Oct 20 '18 at 9:26
  • $\begingroup$ @HKLee. The sphere isn't contractible. $\endgroup$ – Chris Custer Oct 20 '18 at 9:27

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