Assignment:
Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imaginary axes.
The 2 theorems are:
1). Theorem: Suppose f: X --> omega is continuous and X is compact; then f is uniformly continuous. ( of course we are talking about complex plane remember that)
2).Theorem: If A and B are non-empty disjoint sets in X with B closed and A compact then d(A,B) > 0.
Provide complete and step by step solution for the question and show calculations and use formulas.