有序群o-极小展开中可定义的Tietze扩张性质

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2023-05-15 DOI:10.1007/s00153-023-00875-5

Masato Fujita

引用次数: 0

摘要

以下两个断言等价于有序群\(\mathcal M=(M,<,+,0,\ldots )\)的0最小展开。在有界区间和无界区间之间存在一个可定义的双射。定义在\(M^n\)的可定义闭子集上的任何可定义连续函数\(f:A \rightarrow M\)都具有可定义连续扩展\(F:M^n \rightarrow M\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Definable Tietze extension property in o-minimal expansions of ordered groups

The following two assertions are equivalent for an o-minimal expansion of an ordered group \(\mathcal M=(M,<,+,0,\ldots )\). There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function \(f:A \rightarrow M\) defined on a definable closed subset of \(M^n\) has a definable continuous extension \(F:M^n \rightarrow M\).

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.