Vol. 21, No. 3, 1967

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On the Stone-Weierstrass approximation theorem for valued fields

David Geoffrey Cantor

Vol. 21 (1967), No. 3, 473–478

Let X be a compact topological space, L a non-Archimedean rank 1 valued field and F a uniformly closed L-algebra of L-valued continuous functions on X. Kaplansky has shown that if F separates the points of X, then either F consists of all L-valued continuous functions on X or else all of them which vanish on one point in X. In this paper analogous results are obtained, in the case that a group of transformations acts both on X and L, for the invariant L-valued continuous functions on X.

Mathematical Subject Classification
Primary: 12.70
Secondary: 46.00
Received: 11 July 1966
Published: 1 June 1967
David Geoffrey Cantor