Geodesic
The~Nonstandard Hull of a~Normed Space in a~Boolean-valued Universe
Matematičeskie trudy, Tome 4 (2001) no. 2, pp. 42-52

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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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     author = {A. E. Gutman and D. B. Ryabko},
     title = {The~Nonstandard {Hull} of {a~Normed} {Space} in {a~Boolean-valued} {Universe}},
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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/