Banach–Stone theorem

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 from the algebra of scalars (the bounded continuous functions on the space). In modern language, this is the commutative case of the spectrum of a C*-algebra, and the Banach–Stone theorem can be seen as a functional analysis analog of the connection between a ring R and the spectrum of a ring Spec(R) in algebraic geometry.

Banach–Stone theorem

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 from the algebra of scalars (the bounded continuous functions on the space). In modern language, this is the commutative case of the spectrum of a C*-algebra, and the Banach–Stone theorem can be seen as a functional analysis analog of the connection between a ring R and the spectrum of a ring Spec(R) in algebraic geometry.