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

共 11 条

[1]

Aczel P.H.G., 2001, 40 ROYAL SWED AC SCI

[2]

ARMSTRONG MA, 1983, UNDERGRADUATE TEXTS

[3]

Berger J, 2005, J UNIVERS COMPUT SCI, V11, P1878

[4]

Berger J, 2005, LECT NOTES COMPUT SC, V3526, P18

[5]

BERGER J, 2006, FAN THEORETIC EQUIVA

[6] The logical strength of the uniform continuity theorem [J].

Berger, Josef .

LOGICAL APPROACHES TO COMPTATIONAL BARRIERS, PROCEEDINGS, 2006, 3988 :35-39

[7]

Bishop E.A., 1985, GRUNDLEHREN MATH WIS, V279

[8]

Bridges D.S., 1976, B LOND MATH SOC, V8, P179

[9]

Bridges Douglas S., 2006, Techniques of Constructive Analysis

[10]

BRIDGES DS, 1987, LONC MATH SOC LECT N, V97

← 1 2 →