Homotopy

A continuous transformation from one Function to another. A homotopy between two functions $f$ and $g$ from a Space $X$ to a Space $Y$ is a continuous Map $G$ from $X\times[0,1]\mapsto Y$ such that $G(x,0)=f(x)$ and $G(x,1)=g(x)$. Another way of saying this is that a homotopy is a path in the mapping Space $\mathop{\rm Map}(X,Y)$ from the first Function to the second.

See also h-Cobordism