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The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.
Definition source: English Wiktionary via Wiktextract
Topics: complex-analysis, mathematics, sciences, topology
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.
Definition source: English Wiktionary via Wiktextract
Topics: complex-analysis, mathematics, sciences, topology
Examples
- 1967 [Prentice-Hall], Richard A. Silverman, Introductory Complex Analysis, Dover, 1972, page 22, Every circle γ on the Riemann sphere Σ which does not go through a given point P^*∈Σ divides Σ into two parts, such that one part contains P^* and the other does not.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named after German mathematician Bernhard Riemann.
Across languages
Translations
7 source translations are retained for this English entry.
-
Dutch:
Riemann-sfeer
— complex plane with a point at infinity
-
Italian:
sfera di Riemann
— complex plane with a point at infinity
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Polish:
sfera Riemanna
— complex plane with a point at infinity
-
Russian:
сфе́ра Ри́мана
(sféra Rímana)
— complex plane with a point at infinity
-
Italian:
sfera di Riemann
— Euclidean sphere as a representation
-
Polish:
sfera Riemanna
— Euclidean sphere as a representation
-
Russian:
сфе́ра Ри́мана
(sféra Rímana)
— Euclidean sphere as a representation
