Homotopy EquivalentIn topology, a branch of mathematics, two continuous function (topology), continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "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 invariant (mathematics), 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 Spectrum (homotopy theory), spectra. Formal definition Formally, a homotopy between two continuous function (topology), continuous functions ''f'' and ''g'' from a topological space ''X'' to a topological space ''Y'' is defined to be a continuous function H: X \times [0,1] \to Y from the product topology, product of the space ''X'' wit ... [...More Info...] [...Related Items...] |