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A nonstandard characterization of mixed topologies

  • K. D. Stroyan
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 369)

Keywords

Bounded Continuous Function Standard Notion Convex Topology Schwartz Distribution Mackey Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [1]
    Alexiewicz, A., On the two-norm convergence, Studia Math 14 (1953), 49–56.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Alexiewicz, A., and Semadeni, Z., Some properties of two-norm spaces and a characterization of reflexivity of Banach spaces, Studia Math 19 (1960), 115–132.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Buck, R. C., Bounded continuous functions on a locally compact space, Mich. Math. J., 5 (1958), 95–104.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Conway, J. B., The strict topology and compactness in the space of measures II, TAMS 126 (1967), 474–486.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Cooper, J. B., The strict topology and spaces with mixed topologies, PAMS 30 (1971), 583–592.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Dorroh, J. R., The localization of the strict topology via bounded sets, PAMS 20 (1969), 413–414.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Fichtenholz, G., Sur les fonctionnelles linearies continues au sens generalise, Recueil Math 4 (1938), 193–214.zbMATHGoogle Scholar
  8. [8]
    Henson, C. W., and Moore, L. C., Jr., The nonstandard theory of topological vector spaces, TAMS (to appear).Google Scholar
  9. [9]
    Luxemburg, W. A. J., editor, Applications of Model Theory to Algebra, Analysis, and Probability, Holt, Rinehart and Winston, New York, 1969.zbMATHGoogle Scholar
  10. [10]
    Luxemburg, W. A. J., A general theory of monads, in [9].Google Scholar
  11. [11]
    Luxemburg, W. A. J. and Stroyan, K. D., Lecture Notes on Nonstandard Analysis (mimeographed), Caltech bookstore, Pasadena, 1973.Google Scholar
  12. [12]
    Machover, M., and Hirschfeld, J., Lectures on Non-Standard Analysis, Springer-Verlag lecture notes 94, Berlin, 1969.CrossRefzbMATHGoogle Scholar
  13. [13]
    Robinson, A., Non-Standard Analysis, Studies in Logic and the Foundations of Math, North Holland, Amsterdam, 1966.zbMATHGoogle Scholar
  14. [14]
    Robinson, A., and Luxemburg, W. A. J., Contributions to Non-standard Analysis, North Holland, Amsterdam, 1972.zbMATHGoogle Scholar
  15. [15]
    Stroyan, K. D., A characterization of the Mackey uniformity m(L, L1) for finite measures, to appear.Google Scholar
  16. [16]
    Wiweger, A., Linear spaces with mixed topology, Studia Math 20 (1961), 47–68.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Young, L., Functional analysis — a non-standard treatment with semifields, in [14].Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • K. D. Stroyan
    • 1
  1. 1.University of WisconsinMadison

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