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May 17, 2013 at 9:41 comment added Jean Raimbault {\it Autant pour moi}. I will edit the question to ask for compact examples (which I probably should have done in the first place).
May 17, 2013 at 9:36 comment added The User It is contractible, see for example math.ucr.edu/home/baez/week151.html
May 17, 2013 at 9:35 comment added Christian Nassau The infinite dimensional sphere is contractible. And the one point space appears to be another counterexample.
May 17, 2013 at 9:28 comment added Jean Raimbault I don't think this is contractile (in finite dimension it is most certainly not).
May 17, 2013 at 9:24 history answered Swiat Gal CC BY-SA 3.0