Geodesic
Algebraic characterization of finite (branched) coverings
Fundamenta Mathematicae, Tome 158 (1998) no. 2, pp. 165-180
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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.
DOI : 10.4064/fm-158-2-165-180
Keywords: branched covering, open and closed map, ring of continuous functions, flat homomorphism, integral homomorphism 
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M. A. Mulero. Algebraic characterization of finite (branched) coverings. Fundamenta Mathematicae, Tome 158 (1998) no. 2, pp. 165-180. doi: 10.4064/fm-158-2-165-180

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