Homotopy: Difference between revisions
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In [[topology]] two continuous maps <math>f,g:X\to Y</math> are called homotopic if there is a continuous map <math>F:X\times[0,1]\to Y</math> such that <math>f(x)=F(x,0)</math> and <math>g(x)=F(x,1)</math> for all <math>x</math> in <math>X</math>. | In [[topology]] for two topological spaces <math>X</math> and <math>Y</math> two continuous maps <math>f,g:X\to Y</math> are called homotopic if there is a continuous map <math>F:X\times[0,1]\to Y</math> such that <math>f(x)=F(x,0)</math> and <math>g(x)=F(x,1)</math> for all <math>x</math> in <math>X</math>. | ||
Revision as of 02:04, 13 April 2008
In topology for two topological spaces and two continuous maps are called homotopic if there is a continuous map such that and for all in .
![{\displaystyle F:X\times [0,1]\to Y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6409fb7912b4a0028238f262e70e0012cda012f9)
