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Definition: If f and g are continuous maps of the space X into the space Y, we say that f is homotopic to g if there is a continuous map F: XxI -> such that F(x, 0) = f(x) and F(x, 1) = g(x) for each x. (Here I=[0, 1].) The map F is called a homotopy between f and g.
Source: Topology (second edition) by James R. Munkres