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Apartness and Uniformity : A Constructive Development / by Douglas S. Bridges, Luminiţa Simona Vîţă

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Theory and Applications of Computability, In cooperation with the association Computability in Europe | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011Description: Online-Ressource (XIV, 198p. 3 illus, digital)ISBN:
  • 9783642224157
Subject(s): Additional physical formats: 9783642224140 | Buchausg. u.d.T.: Apartness and uniformity. 1. ed. Berlin : Springer, 2011. XIV, 198 S.DDC classification:
  • 004.0151
  • 511.36
MSC: MSC: *03-01 | 54-01 | 03F65RVK: RVK: SK 280 | ST 600LOC classification:
  • QA75.5-76.95
  • QA76
DOI: DOI: 10.1007/978-3-642-22415-7Online resources:
Contents:
Apartness and Uniformity; EPIGRAPH; PREFACE; CONTENTS; 1 THE CONSTRUCTIVE FRAMEWORK; Synopsis; 1.1 Constructivity and Logic; 1.2 Sets and Functions; 1.3 Quasi-metric and Topological Spaces; Notes on Chapter 1; 2 POINT-SET APARTNESS; Synopsis; 2.1 Pre-apartness; 2.2 Apartness and Topology; 2.3 Apartness and Continuity; 2.4 Limits; 2.5 Product Pre-apartness Spaces; 2.6 Concluding Remarks on Impredicativity; Notes on Chapter 2; 3 APARTNESS BETWEEN SETS; Synopsis; 3.1 Set-Set Pre-apartness Relations; 3.2 Quasi-uniform Spaces; 3.3 Strong and Uniform Continuity; 3.4 Convergence of Nets of Functions
3.5 Totally Cauchy Nets3.6 Almost Locatedness; 3.7 Product Apartness Spaces; 3.8 Proximal Connectedness; 3.9 Towards Nearness; 3.10 Neat Compactness; Notes on Chapter 3; POSTLUDE: PATHS TO TOPOLOGY; REFERENCES; INDEX
Summary: Luminiţa Simona VîţăSummary: This book presents a theory of apartness encompassing both point-set topology and the theory of uniform spaces. The first book on the apartness approach to constructive topology, it is a valuable addition to the literature on topology in computer sciencePPN: PPN: 165103916XPackage identifier: Produktsigel: ZDB-2-SCS
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