homotopy
/həˈmɑtəpi/noun
homotopy is a noun meaning “A continuous deformation of one continuous function or map to another” (English Wiktionary, September 2026). It is spelled H-O-M-O-T-O-P-Y, and it appears about once in every 7 million words in written English (wordfreq, 2021 data). The plural of homotopy is homotopies.
What does homotopy mean?
noun
- 1
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.
- 2
The relationship between two continuous functions where homotopy from one to the other is evident.
- 3
informalEllipsis 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.
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
How do you pronounce homotopy?
- US /həˈmɑtəpi/
- US /ˈhoʊmoʊˌtoʊpi/
- US /ˈhoʊmə-/
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Recordings: LL-Q1860_(eng)-Knabrupt-homotopy_(antepenult).wav, LL-Q1860_(eng)-Knabrupt-homotopy.wav, Wikimedia Commons (author and licence on each file's page).
Forms of homotopy
- homotopies plural
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).
How common is homotopy?
Homotopy appears about once in every 7 million words in written English, the 76,798th most frequent word form in the list.
Source: written frequency: wordfreq 3.1 (a 2021 snapshot of Wikipedia, subtitles, news, books, web text and social media).
Homotopy in Spanish, French, German and Portuguese
In the sense (topology) continuous deformation of one continuous function to another:
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract). Translations are Wiktionary's, by sense; a linked word has its own PlainSpell page.
Where does homotopy come from?
From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.
Source: English Wiktionary, dump of September 2, 2026 (CC BY-SA 4.0), through kaikki.org (Wiktextract).