Homotopy

//həˈmɑtəpi// noun, slang

noun, slang ·Moderate ·College level

Definitions

Noun
  1. 1
    A continuous deformation of one continuous function or map to another. countable, uncountable

    "The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another."

  2. 2
    The relationship between two continuous functions where homotopy from one to the other is evident. uncountable
  3. 3
    Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”). abbreviation, alt-of, countable, ellipsis, informal, uncountable
  4. 4
    A theory associating a system of groups with each topological space. countable, uncountable
  5. 5
    A system of groups associated with a topological space. countable, uncountable

Example

More examples

"The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another."

Etymology

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

Related phrases

homotopy categoryhomotopy classhomotopy equivalencehomotopy equivalenthomotopy fiberhomotopy fibrehomotopy grouphomotopy invarianthomotopy relative to a subspacehomotopy theoryhomotopy typelinear homotopy

More for "homotopy"

SynonymsSentencesPronunciationTranslate

Next best steps

Find stronger synonymsSee usage examplesCheck pronunciationBrowse writing guides

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.