Determining continuity complex plane

Reference no: EM13127661

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.

Please I want a very detailed answer and justify every claim or statement in the solution. Please show where each theorem was used and why..I want to fully understand this problem. Thanks.

Polygon is a polygonal line..so Q is composed of lines which are parallel to either the x-axis or y-axis

Reference no: EM13127661

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