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Codimension of some subspaces in a Fréchet algebra

Author: Jens Peter Reus Christensen
Journal: Proc. Amer. Math. Soc. 57 (1976), 276-278
MSC: Primary 46H10
MathSciNet review: 0405107
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Abstract: In a complete separable metrizable topological algebra, if the linear span of the set of all products of two elements has at most countable algebraic codimension, then it has finite codimension.

References [Enhancements On Off] (What's this?)

  • [1] J. P. R. Christensen, Topology and Borel structure, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Descriptive topology and set theory with applications to functional analysis and measure theory; North-Holland Mathematics Studies, Vol. 10. (Notas de Matemática, No. 51). MR 0348724
  • [2] C. Kuratowski, Topologie. Vol. 1, 2nd ed., Monografie Mat., Tom 20, PWN, Warsaw, 1948. MR 10, 389.
  • [3] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
  • [4] Problems list from the conference on derivations and homomorphisms at U.C.L.A., July 1974.

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Article copyright: © Copyright 1976 American Mathematical Society

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