The Theory of Cluster Sets: 56 (Cambridge Tracts in Mathematics)

Book Details

• Author: A. J. Lohwater

• Brand: Cambridge University Press

• Edition: Revised ed.

• Binding: Paperback

• Number of Pages: 224

• Release Date: 03-06-2004

• Languages: English

• ISBN: 9780521604819

About the Book

This book serves as a comprehensive introduction to the theory of cluster sets, a significant branch of topological analysis that has seen remarkable advancements in recent years. The cluster set of a function at a specific point is the set of limit values of the function at that point, which could either be a boundary point or, in the case of non-analytic functions, an interior point of the function's domain.

Cluster sets play an important role in addressing problems that arise in the theory of functions of a complex variable, particularly in the study of boundary behavior, such as the theory of prime ends under conformal mapping. One of the standout features of this work is its detailed discussion of general applications to non-analytic functions, including arbitrary functions, extending the theory beyond traditional analytic functions.

Designed for graduate students, the book assumes a foundational understanding of classical function theory, while including all the specialized material needed to develop a thorough grasp of the theory of cluster sets. Whether you are a student diving into topological analysis or a researcher seeking deeper insights into this fascinating field, this book provides valuable knowledge in an accessible and engaging format.