The Resource Constructive continuity, [by] Mark Mandelkern
Constructive continuity, [by] Mark Mandelkern
Resource Information
The item Constructive continuity, [by] Mark Mandelkern represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Constructive continuity, [by] Mark Mandelkern represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
- eng
- Extent
- v, 117 pages
- Contents
-
- 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
- Isbn
- 9780821822777
- Label
- Constructive continuity
- Title
- Constructive continuity
- Statement of responsibility
- [by] Mark Mandelkern
- Language
- eng
- Summary
- 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
- Cataloging source
- UkLiU
- http://library.link/vocab/creatorDate
- 1933-
- http://library.link/vocab/creatorName
- Mandelkern, Mark
- Index
- no index present
- Literary form
- non fiction
- Series statement
- Memoirs of the American Mathematical Society
- Series volume
- 277
- http://library.link/vocab/subjectName
-
- Functions, Continuous
- Constructive mathematics
- Label
- Constructive continuity, [by] Mark Mandelkern
- Bibliography note
- Includes bibliographical references (pages 111-112), and indexes
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- 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
- Dimensions
- 26 cm.
- Extent
- v, 117 pages
- Isbn
- 9780821822777
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
- Label
- Constructive continuity, [by] Mark Mandelkern
- Bibliography note
- Includes bibliographical references (pages 111-112), and indexes
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- 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
- Dimensions
- 26 cm.
- Extent
- v, 117 pages
- Isbn
- 9780821822777
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Constructive-continuity-by-Mark/48ETpZOF-io/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Constructive-continuity-by-Mark/48ETpZOF-io/">Constructive continuity, [by] Mark Mandelkern</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Constructive-continuity-by-Mark/48ETpZOF-io/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Constructive-continuity-by-Mark/48ETpZOF-io/">Constructive continuity, [by] Mark Mandelkern</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
