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.

Japanese Meaning

複素数全体に∞を加えたもの。複素平面に無限遠点を追加することで得られる数学的対象であり、3次元ユークリッド空間の球面と同相になる。 / トポロジーや複素解析における概念。複素数体を一つの理想的な無限遠点によって拡張したもの。

What is this buttons?

When mapping meromorphic functions to the Riemann sphere, poles correspond to the added point at infinity.

Google Translation / DeepL Translation

メロモルフィック関数を無限遠点を加えた拡大複素平面（無限遠点を含む複素数全体）へ写すと、極は追加された無限遠点に対応します。

Details

Sense（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 Translation / DeepL Translation

Details

Sense（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 Translation / DeepL Translation

Details

Riemann spheres

（ plural ）

Details

Riemann sphere

Dictionary quizzes to help you remember the meaning

Login / Sign up

Download the app!

Riemann sphere

Dictionary quizzes to help you remember the meaning

Login / Sign up

Login

──── or ────

Sign up

──── or ────

Download the app!