homotopy
/həˈmɑtəpi/
homotopy noun: a continuous deformation of one continuous function or map to another. Also the ellipsis of homotopy theory.
Noun
homotopy (countable and uncountable, plural homotopies)
- 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.
- An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.1998, Paul Sellick, “Space Exponents for Loop Spaces of Spheres”, in William G. Dwyer, editor, Stable and Unstable Homotopy, American Mathematical Society, page 279
- The relationship between two continuous functions where homotopy from one to the other is evident.
- A theory associating a system of groups with each topological space.
- A system of groups associated with a topological space.
Also used as
homotopy is also the ellipsis of homotopy theory.
homotopy meaning in Persian and Vietnamese
homotopy in Persian
- (topology) continuous deformation of one continuous function to another
- هموتوپی hemotopi
homotopy in Vietnamese
- (topology) continuous deformation of one continuous function to another
- đồng luân
Forms of homotopy
| plural | homotopies |
|---|
Origin of homotopy
From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.
Words formed from homotopy
- 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
Phrases with homotopy
Questions about homotopy
- What does homotopy mean?
- Homotopy means a continuous deformation of one continuous function or map to another.
- What is homotopy in Persian?
- Homotopy in Persian is هموتوپی (hemotopi). See Homotopy meaning in Persian.
- What part of speech is homotopy?
- Homotopy is a noun.
- How do you pronounce homotopy?
- Homotopy is pronounced /həˈmɑtəpi/ (US).
- What is the plural of homotopy?
- The plural of homotopy is homotopies.
Words near homotopy in the dictionary
Source and license
Adapted from Wiktionary: homotopy (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
Last updated:
Pronunciation audio from Wikimedia Commons, each file under its own free license: LL-Q1860 (eng)-Knabrupt-homotopy (antepenult).wav.
Cite this entry: “homotopy.” Word.ws, https://word.ws/homotopy. Based on Wiktionary, CC BY-SA 4.0.