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  3. The Theory of Cluster Sets
  • Cited by 328
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2009
      January 1966
      ISBN:
      9780511566134
      9780521604819
      DOI:
      https://doi.org/10.1017/CBO9780511566134
      Dimensions:
      Weight & Pages:
      Dimensions:
      (216 x 138 mm)
      Weight & Pages:
      0.294kg, 224 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Real and Complex Analysis
      Series:
      Cambridge Tracts in Mathematics (56)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Real and Complex Analysis
    Series:
    Cambridge Tracts in Mathematics (56)
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    Book description

    The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.

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