Chapter: Topological Aspects
We have already seen that the absolute value induces a metric space on the complex numbers. This fact allows applying many topological concepts also for the complex plane. We restate these concepts here for the special case of complex numbers.
Table of Contents
 Definition: Open and Closed Discs
 Definition: Closed and Open Regions of the Complex Plane
 Definition: Interior, Boundary, and Closures of a Region in the Complex Plane
 Proposition: The distance of complex numbers makes complex numbers a metric space.
 Proposition: Complex Convergent Sequences are Bounded
 Definition: Continuous Functions at Single Complex Numbers
 Proposition: Convergent Complex Sequences Are Cauchy Sequences
 Definition: Complex Sequence
 Definition: Bounded Complex Sequences
 Definition: Convergent Complex Sequence
 Proposition: Convergent Complex Sequences Vs. Convergent Real Sequences
 Definition: Limits of Complex Functions
 Definition: Complex Cauchy Sequence
 Proposition: Complex Cauchy Sequences Vs. Real Cauchy Sequences
 Theorem: Completeness Principle for Complex Numbers
 Definition: Accumulation Points (Complex Numbers)
 Section: Paths
 Section: Homology and Winding Numbers
 Section: Homotopy
 Definition: Bounded Complex Sets
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References
Bibliography
 Riesz F., Sz.Nagy, B.: "Functional Analysis (Translation)", Dover Publications, 1955
 Kneser, Hellmuth: "Mathematische Lehrbücher  Funktionentheorie", Vanderhoeck & Ruprecht, 1958
 Lang, Serge: "Complex Analysis", Springer, 1999, Forth Edition