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.
@article{bwmeta1.element.bwnjournal-article-fmv158i2p165bwm,
author = {M. Mulero},
title = {Algebraic characterization of finite (branched) coverings},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {165-180},
zbl = {0912.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv158i2p165bwm}
}
Mulero, M. Algebraic characterization of finite (branched) coverings. Fundamenta Mathematicae, Tome 158 (1998) pp. 165-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i2p165bwm/
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