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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.

54C35 Function spaces in general topology
46E15 Banach spaces of continuous, differentiable or analytic functions
46E25 Rings and algebras of continuous, differentiable or analytic functions
54D30 Compactness
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