If I take two arbitrary continuous maps ##f,g:S^n\rightarrow S^n## such that ##f(x) \neq -g(x)## for any ##x\in S^n##, then ##f## and ##g## are homotopic.(adsbygoogle = window.adsbygoogle || []).push({});

How do I show this result? I really don't see how to use the condition that ##f## and ##g## never occupy two antipodal points. Any hint would be appreciated.

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# Homotopic maps on a sphere

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