[BibTeX] Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe [in Russian]

Gutman A.E., Ryabko D.B.

Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe [in Russian] //

Proc. Acad. Sci. 2002. V. 384, N 2. P. 153--155.

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@article { Gutman20011224,

author = "Gutman A.E. and Ryabko D.B.",

title = "Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe",

journal = "Proc. Acad. Sci.",

year = "2002",

volume = "384",

number = "2",

pages = "153--155",

language = "russian",

annote = "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."

}