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        "quote": "$\\mathbf{C}P^1$ 与其说是“复平面加一个点”，不如看作一个球面，通常称为[<u class=\"concept-term\" data-concept-reference=\"concepts/topology/complex-projective-space\" data-concept-identity=\"urn:uuid:e663b5dd-c1fb-4282-b563-3b00795ebad3\" data-concept-route=\"/concept-identities#concept-e663b5dd-c1fb-4282-b563-3b00795ebad3\" id=\"first-b695f25c405115c9d415-zh\">黎曼球面(Riemann sphere)</u>](../../../../../concepts/topology/complex-projective-space.md)。球面与复平面及无穷远点之间的关系由[<u class=\"concept-term\" data-concept-reference=\"concepts/geometry/stereographic-projection\" data-concept-identity=\"urn:uuid:6b78393e-3876-49d3-b82b-3dd0d4ff3b21\" data-concept-route=\"/concept-identities#concept-6b78393e-3876-49d3-b82b-3dd0d4ff3b21\" id=\"first-d59757d7da819e92dd76-zh\">球极投影(stereographic projection)</u>](../../../../../concepts/geometry/stereographic-projection.md)给出：从球面北极向球面上各点作直线，并将这些直线投到平面，可在去掉北极的球面与整个平面之间建立一一对应。北极代表无穷远点，因此 $\\mathbf{C}P^1$ 可与 $S^2$ 等同。示意图如下。",
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        "quote": "$\\mathbf{C}P^1$ is better viewed as a sphere, often called the [<u class=\"concept-term\" data-concept-reference=\"concepts/topology/complex-projective-space\" data-concept-identity=\"urn:uuid:e663b5dd-c1fb-4282-b563-3b00795ebad3\" data-concept-route=\"/concept-identities#concept-e663b5dd-c1fb-4282-b563-3b00795ebad3\" id=\"first-b695f25c405115c9d415-en\">Riemann sphere</u>](../../../../../concepts/topology/complex-projective-space.md), rather than as a plane with one extra point. The sphere is related to the plane and its point at infinity by [<u class=\"concept-term\" data-concept-reference=\"concepts/geometry/stereographic-projection\" data-concept-identity=\"urn:uuid:6b78393e-3876-49d3-b82b-3dd0d4ff3b21\" data-concept-route=\"/concept-identities#concept-6b78393e-3876-49d3-b82b-3dd0d4ff3b21\" id=\"first-d59757d7da819e92dd76-en\">stereographic projection</u>](../../../../../concepts/geometry/stereographic-projection.md). Projecting each point of the sphere from the north pole onto the plane gives a one-to-one correspondence between the plane and the sphere with the north pole removed. The north pole represents the point at infinity, so $\\mathbf{C}P^1$ is identified with $S^2$. The picture is shown below.",
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