In topology, two continuous functions from one topological space to another are called homotopic (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 between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.
In practice, there are technical difficulties in using homotopies with certain spaces. Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.
Read more about Homotopy: Formal Definition, Homotopy Equivalence, Homotopy Invariance, Relative Homotopy, Homotopy Groups, Homotopy Category, Timelike Homotopy, Homotopy Lifting Property, Homotopy Extension Property, Isotopy, Applications