A continuous transformation of one function f:X→Y between two topological spaces (or metric spaces) into another function g:X→Y. Formally, a homotopy is a continuous function H:X × [0,1] →Y such that H(x,0) = f(x) and H(x,1) = g(x), and the functions f,g are said to be homotopic, which is written f≃g.