Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The nonstandard theory of topological vector spaces

Authors: C. Ward Henson and L. C. Moore
Journal: Trans. Amer. Math. Soc. 172 (1972), 405-435
MSC: Primary 46A15; Secondary 02H25
Erratum: Trans. Amer. Math. Soc. 184 (1973), 509.
MathSciNet review: 0308722
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the nonstandard theory of topological vector spaces is developed, with three main objectives: (1) creation of the basic nonstandard concepts and tools; (2) use of these tools to give nonstandard treatments of some major standard theorems; (3) construction of the nonstandard hull of an arbitrary topological vector space, and the beginning of the study of the class of spaces which results.

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

  • [1] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. MR 1501880
  • [2] M. M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin, 1958. MR 20 #1187. MR 0094675 (20:1187)
  • [3] C. Ward Henson, The nonstandard hulls of a uniform space, Pacific J. Math. (to appear). MR 0314007 (47:2559)
  • [4] R. C. James, Characterizations of reflexivity, Studia Math. 23 (1963/64), 205-216. MR 30 #431. MR 0170192 (30:431)
  • [5] J. L. Kelley and I. Namioka, Linear topological spaces, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1963. MR 29 #3851. MR 0166578 (29:3851)
  • [6] W. A. J. Luxemburg, A general theory of monads, Internat. Sympos. Applications of Model Theory to Algebra, Analysis, and Probability (Pasadena, Calif., 1967), Holt, Rinehart and Winston, New York, 1969, pp. 18-86. MR 39 #6244. MR 0244931 (39:6244)
  • [7] D. Milman, On some criteria for the regularity of spaces of the type B, C. R. (Dokl.) Acad. Sci. USSR 20 (1938), 243-246.
  • [8] B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Math J. 5 (1939), 249-253. MR 1546121
  • [9] Abraham Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 34 #5680. MR 0205854 (34:5680)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46A15, 02H25

Retrieve articles in all journals with MSC: 46A15, 02H25

Additional Information

Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society