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

title = "The nonstandard hull of a normed space in a Boolean-valued universe",

journal = "Matem. tr.",

year = "2001",

volume = "4",

number = "2",

pages = "42--52",

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.",

keywords = "Boolean-valued analysis, infinitesimal analysis, nonstandard analysis, polyverse, nonstandard hull"