Geodesic
The Nonstandard Hull of a Normed Space in a Boolean-valued Universe
Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 42-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, we extend some results of infinitesimal analysis on normed spaces and the field of reals to the functional representation of a Boolean-valued universe. In particular, we prove equivalence of the following three conditions for an arbitrary polyverse over $Q$: a point $q\in Q$ is not $\sigma$-isolated; the stalk of the polyverse at $q$ is countably saturated; and the nonstandard hull of every normed space in the stalk of the polyverse at $q$ is complete. 
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A. E. Gutman; D. B. Ryabko. The Nonstandard Hull of a Normed Space in a Boolean-valued Universe. Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 42-52. http://geodesic.mathdoc.fr/item/MT_2001_4_2_a2/

[1] Gutman A. E., Losenkov G. A., “Funktsionalnoe predstavlenie bulevoznachnogo universuma”, Mat. trudy, 1:1 (1998), 54–77 | MR | Zbl

[2] Kusraev A. G., Kutateladze S. S., Nestandartnye metody analiza, Nauka, Novosibirsk, 1990 | MR

[3] Hurd A. E., Loeb P. A., An Introduction to Nonstandard Real Analysis, Academic Press, Inc., Orlando, Florida 32887, 1985 | MR | Zbl