Algebraic characterization of finite (branched) coverings

• Autorzy: M. A. Mulero
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
• 54C40: Algebraic properties of function spaces
• 13C10: Projective and free modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 2
• Strony: 165-180

Daty

wydano

1998

otrzymano

1997-08-19

poprawiono

1998-06-22

Twórcy

autor

M. A. Mulero

• Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain

Bibliografia

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