Properties of Riemann Surface
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Theorem
This page gathers some results about Riemann surfaces.
Riemann Surface is Path-Connected
A Riemann surface is path-connected.
Radó's Theorem
A Riemann surface is second countable.
Conformal Isomorphism of Universal Cover of Riemann Surface
The universal cover of a Riemann surface is conformally isomorphic to either:
- the Riemann sphere
- the complex plane
or
- the unit disk.
Riemann Surface is Metrizable
A Riemann surface is metrizable.
Riemann Surface admits Metric of Constant Curvature
A Riemann surface admits a metric of constant curvature.