Integral extensions on rings of continuous functions |
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Authors: | J.M. Domí nguez,M.A. Mulero |
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Affiliation: | a Dpto. de Álgebra, Geometría y Topología, Univ. Valladolid, 47005 Valladolid, Spain b Dpto. de Matemáticas, Univ. Extremadura, 06071 Badajoz, Spain |
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Abstract: | Let π:X→Y be a surjective continuous map between Tychonoff spaces. The map π induces, by composition, an injective morphism C(Y)→C(X) between the corresponding rings of real-valued continuous functions, and this morphism allows us to consider C(Y) as a subring of C(X). This paper deals with finiteness properties of the ring extension C(Y)⊆C(X) in relation to topological properties of the map π:X→Y. The main result says that, for X a compact subset of Rn, the extension C(Y)⊆C(X) is integral if and only if X decomposes into a finite union of closed subsets such that π is injective on each one of them. |
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Keywords: | 54C40 13B21 54D35 |
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