Homotopy

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy (/həˈmɒtəpiː/,^[1] hə-MO-tə-pee; /ˈhoʊmoʊˌtoʊpiː/,^[2] HOH-moh-toh-pee) between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.^[3]

In practice, there are technical difficulties in using homotopies with certain spaces. Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.