On the theorem of Gelfand-Mazur

In its classical statement, the theorem of Gelfand-Mazur is the following: Theorem 1 . — Let $K$ be a complete normed field which is an extension of the field $\mathbf C$ of complex numbers. Then $K=\mathbf C$. As in the history of any theorem, the reality is a bit more complicated. The theorem proved by Stanislas Mazur in 1938 concerns all fields $F$, extensions of the field $\mathbf R$ of real…