I am trying to prove the Riemann mapping theorem for bounded regions by use of the Schwarz-Christoffel formula. Therefore, I need to approximate a given bounded simple connected region by polygons. I know that bounded simply connected regions have a connected boundary. By approximation by polygons I understand a series of polygons which converges into the given region. But i find it hard to show the existence of such a series for any given region with the mentioned conditions. Does someone know a book\article where this problem is discussed or can give me an idea on how to prove it?
2026-03-31 07:56:49.1774943809
Does there always exists a approximation for bounded, simply connected regions by polygons?
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