Homotopy

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In topology for two topological spaces ${\displaystyle X}$ and ${\displaystyle Y}$ two continuous maps ${\displaystyle f,g:X\to Y}$ are called homotopic if there is a continuous map ${\displaystyle F:X\times [0,1]\to Y}$ such that ${\displaystyle f(x)=F(x,0)}$ and ${\displaystyle g(x)=F(x,1)}$ for all ${\displaystyle x}$ in ${\displaystyle X}$.