Ivan Shishkin, Birch Grove

Homotopy

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8/13/2026, 9:15:54 AM · Ancient Tree

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Revision 1239

8/13/2026, 9:11:45 AM · Ancient Tree

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linked exercisesNoneA simple example of homotopy

Revision 1238

8/13/2026, 9:11:24 AM · Ancient Tree

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1An homotopy between two [[Continuous map|continuous maps]] $f,g:X \rightarrow Y$ is a continuous map
2$$H:[0,1]\times X\rightarrow Y$$
3such that $H(0,x)=f(x)$ and $H(1,x)=g(x)$.
4
5##### Remarks
6- If such an homotopy exists, then $f$ and $g$ are said to be homotopic.

Revision 1235

8/13/2026, 9:05:32 AM · Ancient Tree

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An homotopy between two [[Continuous map|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 $H(1,x)=g(x)$.