Overview
- 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
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2208)
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Table of contents (10 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Relational Topology
Authors: Gunther Schmidt, Michael Winter
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-74451-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-74450-6Published: 02 June 2018
eBook ISBN: 978-3-319-74451-3Published: 31 May 2018
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 194
Number of Illustrations: 36 b/w illustrations, 68 illustrations in colour
Topics: Topology, Mathematical Logic and Foundations, Category Theory, Homological Algebra, General Algebraic Systems, Mathematical Applications in Computer Science, Discrete Mathematics