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mathematical analysis > complex analysis > Riemann sphere
... > topology > algebraic topology > manifold > differentiable manifold > complex manifold > Riemann surface > Riemann sphere
... > geometry > topological space > manifold > differentiable manifold > complex manifold > Riemann surface > Riemann sphere
... > geometry > differential geometry > differentiable manifold > complex manifold > Riemann surface > Riemann sphere
... > topology > differential topology > differentiable manifold > complex manifold > Riemann surface > Riemann sphere
geometry > complex geometry > complex manifold > Riemann surface > Riemann sphere
geometry > projective geometry > Riemann sphere

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Riemann sphere  

Definición

  • In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane: the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value ∞ for infinity. With the Riemann model, the point ∞ is near to very large numbers, just as the point 0 is near to very small numbers. The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as 1/0 = ∞ well-behaved. For example, any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is the Riemann sphere.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann_sphere)

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