Homotopy

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In topology for two topological spaces  X {\displaystyle X} and  Y {\displaystyle Y} 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} .