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Variations on the Banach-Stone theorem. (English) Zbl 1027.54021
The authors review some classical and recent contributions concerning extensions, generalizations and variants of the Banach-Stone theorem on determination of the topology of a compact space K by the linear metric structure of C(K). The paper consists of five sections: introduction (a short description of the content), classical results, isometries, algebra isomorphisms, vector lattice isomorphisms. The paper is based on the lectures delivered by the second author in a Summer Course of the University of Cantabria, held in Laredo in August 2001.
MSC:
54C35Function spaces (general topology)
46E15Banach spaces of continuous, differentiable or analytic functions
46E25Rings and algebras of continuous, differentiable or analytic functions
54D30Compactness of topological spaces