The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem

被引：13

作者：

Bridges, Douglas ^{[1
]}

Diener, Hannes ^{[1
]}

机构：

[1] Univ Canterbury, Dept Math & Stat, Christchurch, New Zealand

来源：

JOURNAL OF SYMBOLIC LOGIC | 2007年 / 72卷 / 04期

关键词：

D O I：

10.2178/jsl/1203350793

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every pointwise continuous mapping of [0, 1] into R is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideas.

引用

页码：1379 / 1384

页数：6

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