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The theory of cluster sets

Collingwood, E. F.

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The theory of cluster sets

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The theory of cluster sets/ by E. F. Collingwood and A. J. Lohwater.
作者:	Collingwood, E. F.
其他作者:	Lohwater, A. J.
出版者:	Cambridge :Cambridge University Press, : 1966.,
面頁冊數:	xi, 211 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Cluster set theory. -
電子資源:	https://doi.org/10.1017/CBO9780511566134
ISBN:	9780511566134

The theory of cluster sets
Collingwood, E. F.

The theory of cluster sets[electronic resource] /by E. F. Collingwood and A. J. Lohwater. - Cambridge :Cambridge University Press,1966. - xi, 211 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;56. - Cambridge tracts in mathematics ;56..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511566134Subjects--Topical Terms:

753049
Cluster set theory.

LC Class. No.: QA355 / .C6 1966

Dewey Class. No.: 513.83

The theory of cluster sets
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520 $a 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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