Definition of HOMOTOPY

homotopy

Meanings

Plural: homotopies

Noun

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

Origin / Etymology

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

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