Constructive Notes on Uniform and Locally Convex Spaces

  • Authors:

  • Luminita Dediu;Douglas Bridges

  • Affiliations:

  • -;-

  • Venue:
  • FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
  • Year:
  • 1999

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Abstract

Some elementary notions in the constructive theory of uniform and locally convex spaces are introduced, and a number of basic results established. In particular, it is shown that if the unit ball of a locally convex space X is totally bounded, then so is the intersection of that ball with the kernel of any nonzero continuous linear functional on X.