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Definition: Open and Closed Discs

Let $z\in\mathbb C$ be a complex number and let $r > 0$ be a positive real number. The subset $D\subset\mathbb C$ of the complex plane is called:

• open disc, if $D:=\{\alpha\in\mathbb C\mid |z-\alpha| < r\},$ i.e. if $D$ constitutes open ball in the complex plane.
• closed disc, if $D:=\{\alpha\in\mathbb C\mid |z-\alpha| \le r\}.$

Above, $|\cdot|$ denotes the absolute value of complex numbers.

Example

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Definitions: 1 2 3

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References

Bibliography

1. Lang, Serge: "Algebra - Graduate Texts in Mathematics", Springer, 2002, 3rd Edition
2. Kneser, Hellmuth: "Mathematische Lehrbücher - Funktionentheorie", Vanderhoeck & Ruprecht, 1958