Homotopy

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An homotopy between two continuous maps $f,g:X \rightarrow Y$ is a continuous map
$H:[0,1]\times X\rightarrow Y$ such that $H(0,x)=f(x)$ and $H(1,x)=g(x)$ .

Remarks

If such an homotopy exists, then $f$ and $g$ are said to be homotopic.

Practice this concept with exercises

Are the maps $f,g:\R \rightarrow \R$ given by $f(x)=x^{2}$ and $g(x)=(x+1)^{2}$ homotopic?

The graph of f (green) and g (red).

Open exerciseDifficulty 29/100 · 1 solution · 0 hints

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