KnowraHomotopy equivalenceLinked fromLinked fromThe 9 pages that link to Homotopy equivalence, each with the reason it gives.All 9Broader topic 3Related 2Compared with 4HomeomorphismCompared with: It is weaker than homeomorphism: spaces can be homotopy equivalent without being homeomorphic.Algebraic topologyCompared with: It defines a coarser notion of sameness than homeomorphism, the usual target of homotopy invariants.IsomorphismCompared with: It can identify spaces up to continuous deformation without requiring a homeomorphism.Excision theoremCompared with: It gives homology isomorphisms by comparing whole spaces up to deformation.