Definitions for "Homotopy"
A continuous transformation from one mapping to another. One example is the convex combination: (x) + (1-t)(x). As t varies from 0 to 1, the function changes continuously from to .
See Homotopic maps.
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 is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.