The Theory of Cluster Sets (Cambridge Tracts in Mathematics, Series Number 56)
ISBN-13:
9780521604819
ISBN-10:
0521604818
Author:
E. F. Collingwood, A. J. Lohwater
Publication date:
2004
Publisher:
Cambridge University Press
Format:
Paperback
224 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
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Book details
ISBN-13:
9780521604819
ISBN-10:
0521604818
Author:
E. F. Collingwood, A. J. Lohwater
Publication date:
2004
Publisher:
Cambridge University Press
Format:
Paperback
224 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
Summary
The Theory of Cluster Sets (Cambridge Tracts in Mathematics, Series Number 56) (ISBN-13: 9780521604819 and ISBN-10: 0521604818), written by authors
E. F. Collingwood, A. J. Lohwater, was published by Cambridge University Press in 2004.
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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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