Geodesic
On Nonstandard Hulls of Convex Spaces
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 141-147

Voir la notice de l'article provenant de la source Cambridge University Press

A nonstandard hull of a TVS (locally convex topological vector space) is a standard TVS constructed from a nonstandard model for [3]. If the nonstandard hulls of a TVS are independent of the non-standard model, we say that the TVS has invariant nonstandard hulls. This is (for complete spaces) the property that every finite element is inflnitesimally close to a standard point. We build on the work of Henson and Moore [4], to show that invariance of nonstandard hulls is a self dual property equivalent to bounded sets being precompact, for F and DF spaces, (see Theorem 4.4). 
Bellenot, Steven F. On Nonstandard Hulls of Convex Spaces. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 141-147. doi: 10.4153/CJM-1976-017-x
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[1] 1. Bellenot, S. F., Prevarieties and interwinded completeness of locally convex spaces, Math. Ann. 217 (1975), 59–67, Google Scholar

[2] 2. Berenzanskii, LA., Inductively reflexive locally convex spaces, Soviet Math. Doklady (Translations from Russian) 9(2) (1968), 1080–1082. Google Scholar

[3] 3. Henson, C. W. and M∞re, L. C., Jr., The theory of nonstandard topological vector spaces, Trans. Amer. Math. Soc. 172 (1972), 193–206. Google Scholar

[4] 4. Invariance of the nonstandard hulls of locally convex spaces, Duke Math. J. 4-0 (1973), 193–206. Google Scholar

[5] 5. Hogbe-Nlend, H., Topologies et homologies nucléaires associées applications, Ann. Inst. Fourier (Grenoble) 23 (1973), fasc. 4, 89–104. Google Scholar

[6] 6. Horvath, J., Topological vector spaces and distributions (Addison-Wesley, Reading, Mass., vol. I 1966). Google Scholar

[7] 7. Kôthe, G., Topological vector spaces, I (Springer-Verlag, New York, 1969). Google Scholar

[8] 8. Peitsch, A., Nuclear locally convex spaces (Springer-Verlag, New York, 1972). Google Scholar

[9] 9. Robertson, A. P. and Robertson, W. J., Topological vector spaces, 2nd edition (Cambridge University Press, London, 1973). Google Scholar

[10] 10. Robinson, A., Nonstandard analysis (North Holland, Amsterdam, 1968). Google Scholar

[11] 11. Robinson, A. and Zakon, E., A set-theoretical characterization of enlargements, Applications of model theory (Holt, Rinehart and Winston, New York, 1969), 109–122. Google Scholar

[12] 12. Terzioglu, T., On Schwartz spaces, Math. Ann. 182 (1969), 236–242. Google Scholar

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