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ArticleOriginal scientific text

Title

Algebraic characterization of finite (branched) coverings

Authors 1

Affiliations

  1. Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

Abstract

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism C(S) → C(X) is integral and flat.

Keywords

ENG
branched covering, open and closed map, ring of continuous functions, flat homomorphism, integral homomorphism

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Fundamenta Mathematicae
1998/158/2
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Pages:
165-180
Main language of publication
English
Received
1997-08-19
Accepted
1998-06-22
Published
1998
Exact and natural sciences