|
This article is cited in 1 scientific paper (total in 1 paper)
The Nonstandard Hull of a Normed Space in a Boolean-valued Universe
A. E. Gutmana, D. B. Ryabkob a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
Abstract:
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.
Key words:
Boolean-valued analysis, infinitesimal analysis, nonstandard analysis, polyverse, nonstandard hull.
Received: 19.02.2001
Citation:
A. E. Gutman, D. B. Ryabko, “The Nonstandard Hull of a Normed Space in a Boolean-valued Universe”, Mat. Tr., 4:2 (2001), 42–52; Siberian Adv. Math., 12:2 (2002), 38–47
Linking options:
https://www.mathnet.ru/eng/mt12 https://www.mathnet.ru/eng/mt/v4/i2/p42
|
Statistics & downloads: |
Abstract page: | 245 | Full-text PDF : | 92 | References: | 46 | First page: | 1 |
|