Abstract
In this chapter, we address the natural problem of determining conditions for a topological surface to admit a holomorphic structure. One necessary condition is, of course, that the surface be orientable. According to Radó’s theorem (Theorem 2.11.1), another necessary condition is that the surface be second countable. It turns out that these two conditions are also sufficient.
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Napier, T., Ramachandran, M. (2011). Holomorphic Structures on Topological Surfaces. In: An Introduction to Riemann Surfaces. Cornerstones. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4693-6_6
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DOI: https://doi.org/10.1007/978-0-8176-4693-6_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4692-9
Online ISBN: 978-0-8176-4693-6
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