English Explanatory Dictionary

homotopy

English dictionary entry

Meanings

noun
  1. A continuous deformation of one continuous function or map to another.
  2. The relationship between two continuous functions where homotopy from one to the other is evident.
  3. Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
  4. A theory associating a system of groups with each topological space.
  5. A system of groups associated with a topological space.

Pronunciation

/həˈmɑtəpi/ /ˈhoʊmoʊˌtoʊpi/ /ˈhoʊmə-/ LL-Q1860 (eng)-Knabrupt-homotopy (antepenult).wav LL-Q1860 (eng)-Knabrupt-homotopy.wav

Word forms

homotopy homotopies

Etymology

From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.

Related words

homotopic homeotopy group homology

Derived words

cohomotopy homotopic homotopy category homotopy class homotopy equivalence homotopy equivalent homotopy fiber homotopy fibre homotopy group homotopy invariant homotopy relative to a subspace homotopy theory homotopy type linear homotopy regular homotopy straight-line homotopy

Translations

French: homotopie Hungarian: homotópia Spanish: homotopía
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