Banach–Stone theorem.

About Banach–Stone theorem

An important question in mathematics is whether a space can be completely described by the functions defined on it—that is, by its "observables." The Banach–Stone theorem is a classical result in this direction. It shows that certain well-behaved spaces can be recovered from the Banach space of continuous functions defined on them. The theorem is named after the mathematicians Stefan Banach and Marshall Stone.