homotopy.
A continuous deformation of one continuous function or map to another.
Meaning & usage
A continuous deformation of one continuous function or map to another.
The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into 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.
Where this word comes from
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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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.