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Cluster Sets of Pseudomeromorphic Functions

Published online by Cambridge University Press:  22 January 2016

D. A. Storvick
D. A. Storvick*
Affiliation:
Department of Mathematics, University of Minnesota
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Let w = f(z) = u(x, y) + iv(x, y) be an interior transformation in the sense of Stoïlow in an arbitrary domain D, i.e. w = f(z) is continuous and single-valued in D, and unless constant takes open sets in D into open sets in the w-plane, and does not take any continuum (other than a single point) into a single point of the w-plane. Stoïlow proved that such an interior transformation can be represented as

where T(z) = ξ is a topological mapping of D onto a domain D′ and w = φ(ξ) is a meromorphic function in D′.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 18 , April 1961 , pp. 43 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

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