Definition: Interior, Boundary, and Closures of a Region in the Complex Plane

Let $U\subseteq\mathbb C$ be a subset of the complex plane. * A point $b\in U$ is said to be in the interior of $U$, if there is a disc $B(b,r)$ contained in $U.$ * A point $b$ is called a boundary point of $U,$ if every disc centered at $b$ contains both, the points of the interior of $U$ and outside the interior of $U.$ * The closure of $U$ is the set union of $U$ with its boundary points.

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References

Bibliography

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  2. Kneser, Hellmuth: "Mathematische Lehrb├╝cher - Funktionentheorie", Vanderhoeck & Ruprecht, 1958
  3. Lang, Serge: "Complex Analysis", Springer, 1999, Forth Edition