TITLE: How to show $S^n$ is not contractible without using Homology..
QUESTION [6 upvotes]: I know the prove $S^n$ is not contractible using homology.But I don't know how to prove it from definition of contractibility.Can anyone help me in this direction?
Thanks.

REPLY [9 votes]: Following is taken from Fixed point theory - Dugundji, p. 95.
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