- Introduces and develops an algebraic treatment of Boolean matrices
- Applies the methods to give an algebraic treatment of point set topology
- Offers a framework for handling topological problems using theorem provers
- Includes nearly 100 diagrams of relations presented as matrices
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- Über dieses Buch
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This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science.
Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
- Inhaltsverzeichnis (10 Kapitel)
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Introduction
Seiten 1-6
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Prerequisites
Seiten 7-24
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Products of Relations
Seiten 25-44
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Meet and Join as Relations
Seiten 45-66
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Applying Relations in Topology
Seiten 67-97
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Inhaltsverzeichnis (10 Kapitel)
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Bibliografische Information
- Bibliographic Information
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- Buchtitel
- Relational Topology
- Autoren
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- Gunther Schmidt
- Michael Winter
- Titel der Buchreihe
- Lecture Notes in Mathematics
- Buchreihen Band
- 2208
- Copyright
- 2018
- Verlag
- Springer International Publishing
- Copyright Inhaber
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-74451-3
- DOI
- 10.1007/978-3-319-74451-3
- Softcover ISBN
- 978-3-319-74450-6
- Buchreihen ISSN
- 0075-8434
- Auflage
- 1
- Seitenzahl
- XIV, 194
- Anzahl der Bilder
- 36 schwarz-weiß Abbildungen, 68 Abbildungen in Farbe
- Themen
