New non-standard topologies

被引：2

作者：

Khalfallah, Adel ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 172卷 / 3-4期

关键词：

Non-standard analysis; S-topology; Q-topology; Robinson's asymptotic numbers; GENERALIZED-FUNCTIONS; FUNCTORIALITY; ALGEBRA; FIELDS;

D O I：

10.1007/s00605-013-0494-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, on a non-standard extension of a metric space , we construct a chain of new non-standard topologies in terms of convex subrings of , its minimal element is the -topology and its maximal is the -topology. Next, we construct , the -asymptotic hull of , and we prove that such space is metrizable and complete when is generated by an asymptotic scale. Finally, we provide a pseudo-valuation taking integral values, equivalent to the classical Robinson's valuation, on , the Robinson's field of -asymptotic numbers.

引用

页码：323 / 344

页数：22

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