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What is Connectedness in Complex Analysis about?

This document summarizes the proof of Theorem II.2.3, which states that an open set G in C is connected if and only if for any two points a, b in G there is a polygon from a to b lying entirely in G. The proof first assumes G is not connected, then uses this assumption to derive a contradiction by showing [0,1] cannot be separated into disjoint open sets, proving G must be connected. It then shows if G is open and connected, there is a polygon between any a, b in G.

Author

TOM DAVIS

Language

EN