Pacific Journal of Mathematics

The Stone-Weierstrass theorem for valuable fields.

P. R. Chernoff, R. A. Rasala, and W. C. Waterhouse

Article information

Pacific J. Math., Volume 27, Number 2 (1968), 233-240.

First available in Project Euclid: 13 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12.70


Chernoff, P. R.; Rasala, R. A.; Waterhouse, W. C. The Stone-Weierstrass theorem for valuable fields. Pacific J. Math. 27 (1968), no. 2, 233--240.

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  • [1] N. Bourbaki, Algebre Commutative, Chap. VI, Hermann, Paris, 1964.
  • [2] D. G. Cantor, On the Stone-Weierstrassapproximation theorem for valued fields, Pacific J. Math. 21 (1967), 473-478.
  • [3] J. Dieudonne, Sur les functions continues p-adiques, Bull. Sci. Math. (2) 68 (1944), 79-95.
  • [4] I. Kaplansky, The Weierstrass theorem in fields with valuations, Proc. Amer. Math. Soc. 1 (1950), 356-357.
  • [5] K. Mahler, An interpolation series for a continuous function of a p-adic variable, J. Reine u. Angew. Math. 199 (1958), 23-34.
  • [6] M. H. A. Newman, Elements of the Topology of Plane Sets of Points, 2nd ed., Cambridge Univ. Press, Cambridge, 1961.
  • [7] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
  • [8] M. H. Stone, A generalized Weierstrass approximation theorem, Studies in Modern Analysis (Mathematical Assoc. of America), Prentice-Hall, Englewood Cliffs, N. J., 1962.