Constructive continuity

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There are two long outstanding constructivity problems concerning real-valued functions on the closed unit interval: (i) is every function continuous? (ii) is every continuous function uniformly continuous? In this paper the method of reliefs is introduced to aid the study of these problems. While so far leading to no definitive solutions, the method has yielded a few partial results, and might be used as a basis for further investigations.

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Title Statements

Full title :Constructive continuity / Mark Mandelkern.

Summary

Edition Statements

Publication Date:©1983.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, R.I
Language:eng
Publication Date:©1983.

The Physical Object

Description:v, 117 pages ; : 26 cm.

Edition Identifiers

ISBN:0821822772, 9780821822777
oclc:ocm09111970
LC Classification:QA3
Dewey Decimal:510 s

Problems, methods, and main results -- Part I. Preliminaries ; Brouwerian counterexamples -- Real numbers -- Infima and suprema -- Metric spaces -- Part II. Reliefs and continuous functions ; Reliefs - Continuity -- Intermediate values -- Bounds and extremes -- Connectivity and convexity -- Located sets -- Part III. Monotone functions ; Monotonicity -- Monotonicity and continuity -- Part IV. Relief functions and the limited continuity principle ; Relief functions -- Existence of relief functions -- The limited continuity principle.