Riemann Surface is Path-Connected
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Theorem
A Riemann surface is path-connected.
Proof
By definition, a Riemann surface is a complex manifold.
Hence it is connected and locally path-connected.
This article, or a section of it, needs explaining. In particular: It needs to be established that a complex manifold indeed has both of these properties. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
This theorem requires a proof. In particular: A link needed to a page which derives the fact of path-connectedness from connectedness and local path-connectedness. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |