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Sequential, pointwise, and uniform continuity: A constructive note

 

作者: Douglas S. Bridges,  

 

期刊: Mathematical Logic Quarterly  （WILEY Available online 1993）
卷期: Volume 39, issue 1  

页码: 55-61

 

ISSN:0942-5616

 

年代: 1993

 

DOI:10.1002/malq.19930390108

 

出版商: WILEY‐VCH Verlag Berlin GmbH

 

关键词: Constructive analysis;Sequential continuity;Pointwise continuity;Uniform continuity

 

数据来源: WILEY

 

摘要:

AbstractThe main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real‐valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S3

 

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