On uniformly continuous functions between pseudometric spaces and the Axiom of Countable Choice

被引：2

作者：

da Silva, Samuel G. ^{[1
]}

机构：

[1] Univ Fed Bahia Campus Ondina, Inst Matemat, Av Adhemar de Barros S-N, BR-40170110 Salvador, BA, Brazil

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2019年 / 58卷 / 3-4期

关键词：

Axiom of Countable Choice; Pseudometric spaces; Uniform continuity;

D O I：

10.1007/s00153-018-0643-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between (pseudo)metric spaces, and the second declares that sequentially compact pseudometric spaces are UC-meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous.

引用

页码：353 / 358

页数：6

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