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On the Topological Theory of Functions

Published online by Cambridge University Press:  20 November 2018

James A. Jenkins
James A. Jenkins*
Affiliation:
Johns Hopkins University
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The present paper constitutes a continuation of the ideas and methods of M. Morse and M. Heins [1]. As in that work the subject treated is the theory of deformation classes of meromorphic functions and interior transformations. There the functions considered were defined over the open disc < 1 and had only a finite number of zeros, poles and branch point antecedents. It is possible to transfer the results obtained to the situation where the domain of definition is any simply-connected domain of hyperbolic type or, alternatively, of parabolic type.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 276 - 289
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Morse, M. and Heins, M., Deformation classes of meromorphic functions and their extensions to interior transformations, Acta Math., vol. 79 (1947), 51–103.Google Scholar
[2] Morse, M., Topological methods in the theory of meromorphic functions, Ann. of Math. Studies (Princeton, N.J., 1947).Google Scholar
[3] v., Kerékjártό|B., Vorlesungen ilber Topologie (Berlin, 1923).Google Scholar
[4] Stoïlow, S., Leçons sur les principes topologiques de la théorie des fonctions analytiques (Paris, 1938).Google Scholar
[5] Tietze, H., Sur les reprçsentations continues des surfaces sur elles-mêmes, Comptes Rendus 157 (1913), 509–512.Google Scholar
[6] Dienes, P., The Taylor Series (Oxford, 1931)Google Scholar