In topology two continuous maps f , g : X → Y {\displaystyle f,g:X\to Y} are called homotopic if there is a continuous map F : X × [ 0 , 1 ] → Y {\displaystyle F:X\times [0,1]\to Y} such that f ( x ) = F ( x , 0 ) {\displaystyle f(x)=F(x,0)} and g ( x ) = F ( x , 1 ) {\displaystyle g(x)=F(x,1)} for all x {\displaystyle x} in X {\displaystyle X} .
![{\displaystyle F:X\times [0,1]\to Y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6409fb7912b4a0028238f262e70e0012cda012f9)
