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Algebraic characterization of finite (branched) coverings

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Mulero M. A.

Fundamenta Mathematicae

1998

tom 158

nr 2

165-180

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Mulero M. A.

1 1998

Wyniki wyszukiwania

Algebraic characterization of finite (branched) coverings