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Homotopy vs Homeomorphism - What's the difference?

homotopy | homeomorphism |

In topology terms the difference between homotopy and homeomorphism

is that homotopy is a system of groups associated to a topological space while homeomorphism is a continuous bijection from one topological space to another, with continuous inverse.

homotopy

English

(wikipedia homotopy)

Noun

(homotopies)
  • (topology) A continuous deformation of one continuous function to another.
  • (topology) A theory associating a system of groups to each topological space.
  • (topology) A system of groups associated to a topological space.

    • Hyponyms

    * (continuous deformation) isotopy

    homeomorphism

    English

    Alternative forms

    * homoeomorphism (UK) *

    Noun

    (en noun)
  • (topology) a continuous bijection from one topological space to another, with continuous inverse.
  • (chemistry) a similarity in the crystal structure of unrelated compounds

    • See also

    * ("homeomorphism" on Wikipedia) * diffeomorphism