In topology, two continuous functions from one topological space to another are called homotopic (Greek homos = identical and topos = place) if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions. An outstanding use of homotopy's the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there're technical difficulties in using homotopies with certain pathological spaces.… (More on Homotopy)