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hadroneater
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Homework Statement
Let S be the open unit disk of radius 2 centered at the origin. T is a subset of the real axis. The set R is obtained by removing T from S. Is R a domain when:
1. T is the line segment {z[itex]\in[/itex] ℂ | Re(z) ≤ 1 and Im(z) = 0}
2. T is the line segment {z[itex]\in[/itex] ℂ | Re(z) < 2 and Im(z) = 0}
Homework Equations
A set R is domain when it is open and connected.
The Attempt at a Solution
The problem is I've never taken a rigorous course on sets or proofs so I have very little knowledge in terms of how to see whether a set if open/connected.
1. It is a closed set because of the new boundary of S in the form of T.
2. It is open because Re(z) < 2 is included in the origin boundary for S.