A local stability principle for continuous group homomorphisms in nonstandard setting

被引：0

作者：

Filip Sládek

Pavol Zlatoš

机构：

[1] Comenius University,Faculty of Mathematics, Physics and Informatics

来源：

Aequationes mathematicae | 2015年 / 89卷

关键词：

Nonstandard analysis; topological group; continuous homomorphism; stability; Primary 22D12; Secondary 54J05; 22C05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We state a simple fact relating some continuity and homomorphy properties of an internal mapping between nonstandard extensions of topological groups and the nonstandard extension of the “observable trace” of the map, which can be interpreted as a kind of stability principle. This leads to a strengthening of two formerly proved (standard) stability results (a global one and a local one) along with simplifying their proofs. We show that every “sufficiently continuous,” “reasonably bounded” and “sufficiently homomorphic” mapping from a locally compact to an arbitrary topological group is “arbitrarily close” to a continuous homomorphism between them.

引用

页码：991 / 1001

页数：10

共 15 条

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