Riemann sphere

noun

(topology, complex analysis) 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.

The Riemann sphere is a compactification of the complex plane.

Google翻訳 / DeepL翻訳

詳細

意味（1）

We use ̂Complex^⨯ (resp. Complex ) to denote the subset z∈̂ Complex :z ne 0 (resp. z∈̂ Complex :z ne ∞) in the Riemann sphere ̂ Complex .

Google翻訳 / DeepL翻訳

詳細

意味（2）

(topology, complex analysis) 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.

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.

Google翻訳 / DeepL翻訳

詳細

Riemann sphere

Dictionary quizzes to help you remember the meaning

ログイン / 新規登録

アプリをダウンロード！

Riemann sphere

Dictionary quizzes to help you remember the meaning

ログイン / 新規登録

ログイン

──── or ────

新規登録

──── or ────

アプリをダウンロード！