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The nonstandard theory of topological vector spaces. (English) Zbl 0254.46001


MSC:

46A03 General theory of locally convex spaces
03H99 Nonstandard models
26E35 Nonstandard analysis
54J05 Nonstandard topology
46B10 Duality and reflexivity in normed linear and Banach spaces
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[1] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396 – 414. · Zbl 0015.35604
[2] Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[3] C. Ward Henson, The nonstandard hulls of a uniform space, Pacific J. Math. 43 (1972), 115 – 137. · Zbl 0245.54046
[4] R. C. James, Characterizations of reflexivity, Studia Math. 23 (1963/1964), 205 – 216. · Zbl 0113.09303
[5] J. L. Kelley and Isaac Namioka, Linear topological spaces, With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. · Zbl 0115.09902
[6] W. A. J. Luxemburg, A general theory of monads, Applications of Model Theory to Algebra, Analysis, and Probability (Inte rnat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 18 – 86.
[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. · Zbl 0019.41601
[8] B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Math. J. 5 (1939), no. 2, 249 – 253. · Zbl 0021.32601 · doi:10.1215/S0012-7094-39-00522-3
[9] Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. · Zbl 0102.00708
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