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 50 条

[41] A theorem of Littlewood, Orlicz, and Grothendieck about sums in L1(0,1)
Diestel, J
Fourie, J
Swart, J
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (01) : 376 - 394
[42] Decidable fan theorem and uniform continuity theorem with continuous moduli
Fujiwara, Makoto
Kawai, Tatsuji
MATHEMATICAL LOGIC QUARTERLY, 2021, 67 (01) : 116 - 130
[43] (0,1)-MATRICES
KHOMENKO, NP
VYVROT, TM
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1976, (10): : 887 - 889
[44] De Finetti theorem and Borel states in [0,1]-valued algebraic logic
Kuehr, Jan
Mundici, Daniele
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2007, 46 (03) : 605 - 616
[45] FFD BIN PACKING FOR ITEM SIZES WITH UNIFORM DISTRIBUTIONS ON [0,1/2]
FLOYD, S
KARP, RM
ALGORITHMICA, 1991, 6 (02) : 222 - 240
[46] Approximation Theorem for New Modification of q-Bernstein Operators on (0,1)
Wu, Yun-Shun
Cheng, Wen-Tao
Chen, Feng-Lin
Zhou, Yong-Hui
JOURNAL OF FUNCTION SPACES, 2021, 2021
[47] (0,1)-MATRICES
JAGERS, AA
AMERICAN MATHEMATICAL MONTHLY, 1979, 86 (06): : 505 - 506
[48] REPRESENTATION THEOREM FOR FINITE MARKOV CHAINS WHOSE STATES ARE SUBINTERVALS OF [0,1]
SENGUPTA, SS
CZARNY, P
CHOW, R
INFORMATION SCIENCES, 1971, 3 (01) : 51 - &
[49] Beurling's theorem for the Hardy operator on L2[0,1]
Agler, Jim
McCarthy, John E. E.
ACTA SCIENTIARUM MATHEMATICARUM, 2023, 89 (3-4): : 573 - 592
[50] ON THE RATE OF CONVERGENCE IN CENTRAL LIMIT-THEOREM IN THE SPACE D[0,1]
PAULAUSKAS, VI
IUKNIAVICHENE, DB
DOKLADY AKADEMII NAUK SSSR, 1989, 307 (03): : 545 - 547

← 1 2 3 4 5 →