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Covering properties of open continuous mappings having two valences between Riemann surfaces

Published online by Cambridge University Press:  24 October 2008

Abdallah Lyzzaik
Abdallah Lyzzaik
Affiliation:
Department of Mathematics, American University of Beirut, Beirut, Lebanon
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Abstract

Let be an open Riemann surface with finite genus and finite number of boundary components, and let be a closed Riemann surface. An open continuous function from to is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in either p or q times, counting multiplicity, with possibly a finite number of exceptions. These comprise the most general class of all non-trivial functions having two valences between and .

The object of this paper is to study the geometry of (p, q)-maps and establish a generalized embedding theorem which asserts that the image surfaces of (p, q)-maps embed in p-fold closed coverings possibly having branch points off the image surfaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 321 - 340
Copyright
Copyright © Cambridge Philosophical Society 1995

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