最終更新日：2024/08/03

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(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.

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Riemann sphere

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Riemann sphere

noun

The Riemann sphere is a compactification of the complex plane.

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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 .

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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.

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Riemann sphere

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