Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.
A continuous deformation of one continuous function or map to another.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: mathematics, sciences, topology
Examples
- The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
- 2010, Vladimir G. Turaev, Homotopy Quantum Field Theory, European Mathematical Society, page xi, In this monograph we apply the idea of a TQFT to maps from manifolds to topological spaces. This leads us to a notion of a (d + 1)-dimensional homotopy quantum field theory (HQFT) which may be described as a TQFT for closed oriented d-dimensional manifolds and compact oriented (d + 1)-dimensional cobordisms endowed with maps to a given space X.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The relationship between two continuous functions where homotopy from one to the other is evident.
Definition source: English Wiktionary via Wiktextract
Usage: uncountable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
Definition source: English Wiktionary via Wiktextract
Usage: abbreviation, alt-of, countable, ellipsis, informal, uncountable
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
A theory associating a system of groups with each topological space.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: mathematics, sciences, topology
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
A system of groups associated with a topological space.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Topics: mathematics, sciences, topology
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.
Across languages
Translations
19 source translations are retained for this English entry.
-
Danish:
homotopi
— (topology) continuous deformation of one continuous function to another
-
French:
homotopie
— (topology) continuous deformation of one continuous function to another
-
Greek:
ομοτοπία
(omotopía)
— (topology) continuous deformation of one continuous function to another
-
Hungarian:
homotópia
— (topology) continuous deformation of one continuous function to another
-
Icelandic:
samtogun
— (topology) continuous deformation of one continuous function to another
-
Japanese:
ホモトピー
— (topology) continuous deformation of one continuous function to another
-
Korean:
연속 변형 함수
(yeonsok byeonhyeong hamsu)
— (topology) continuous deformation of one continuous function to another
-
Korean:
호모토피
(homotopi)
— (topology) continuous deformation of one continuous function to another
-
Persian:
هموتوپی
(hemotopi)
— (topology) continuous deformation of one continuous function to another
-
Portuguese:
homotopia
— (topology) continuous deformation of one continuous function to another
-
Spanish:
homotopía
— (topology) continuous deformation of one continuous function to another
-
Ukrainian:
гомотопія
(homotopija)
— (topology) continuous deformation of one continuous function to another
-
Vietnamese:
đồng luân
— (topology) continuous deformation of one continuous function to another
-
French:
homotopie
— (topology) theory associating a system of groups with each topological space
-
Hungarian:
homotópia
— (topology) theory associating a system of groups with each topological space
-
Spanish:
homotopía
— (topology) theory associating a system of groups with each topological space
-
French:
homotopie
— (topology) system of groups associated with a topological space
-
Hungarian:
homotópia
— (topology) system of groups associated with a topological space
-
Spanish:
homotopía
— (topology) system of groups associated with a topological space
