: Mathematics: Riemann surface

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... > topological space > manifold > differentiable manifold > complex manifold > Riemann surface

geometry > differential geometry > differentiable manifold > complex manifold > Riemann surface

topology > differential topology > differentiable manifold > complex manifold > Riemann surface

geometry > complex geometry > complex manifold > Riemann surface

Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
Loosely speaking, this means that any Riemann surface is formed by gluing together open subsets of the complex plane C using holomorphic gluing maps.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann_surface)

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