Concept information
Preferred term
Banach-Stone theorem
Definition(s)
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In mathematics, the Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and Marshall Stone. In brief, the Banach–Stone theorem allows one to recover a compact Hausdorff space X from the Banach space structure of the space C(X) of continuous real- or complex-valued functions on X. If one is allowed to invoke the algebra structure of C(X) this is easy – we can identify X with the spectrum of C(X), the set of algebra homomorphisms into the scalar field, equipped with the weak*-topology inherited from the dual space C(X)*. The Banach-Stone theorem avoids reference to multiplicative structure by recovering X from the extreme points of the unit ball of C(X)*.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Banach%E2%80%93Stone_theorem)
Broader concept(s)
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-TJ96QCNN-G
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