Connectedness, Convexity, Analyticity

John Mac Sheridan Nerney
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John Mac Sheridan Nerney: Mathematics

Chapter Chapter 4 in An Introduction to Analytic Functions, 2020, pp 25-28 from Springer

Abstract: Abstract Two subsets of ℂ $$\mathbb C$$ are mutually separated Mutually separated sets provided neither of them contains a point or a limit-point of the other. A subset of ℂ $$\mathbb C$$ is connected Connected set provided it is not the union of two nonempty and mutually separated sets. A component Component of a set of the subset S ⊆ ℂ $$S\subseteq \mathbb C$$ is a connected subset of S which is not a proper subset of any connected subset of S. In other words, when the collection of connected subsets of S is partially ordered by containment, the components are maximal elements.

Date: 2020
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DOI: 10.1007/978-3-030-42085-7_5

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