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Relational Topology

  • Gunther Schmidt
  • Michael Winter

Part of the Lecture Notes in Mathematics book series (LNM, volume 2208)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Gunther Schmidt, Michael Winter
    Pages 1-6
  3. Gunther Schmidt, Michael Winter
    Pages 7-24
  4. Gunther Schmidt, Michael Winter
    Pages 25-44
  5. Gunther Schmidt, Michael Winter
    Pages 45-66
  6. Gunther Schmidt, Michael Winter
    Pages 67-97
  7. Gunther Schmidt, Michael Winter
    Pages 99-111
  8. Gunther Schmidt, Michael Winter
    Pages 113-124
  9. Gunther Schmidt, Michael Winter
    Pages 125-143
  10. Gunther Schmidt, Michael Winter
    Pages 145-153
  11. Gunther Schmidt, Michael Winter
    Pages 155-181
  12. Back Matter
    Pages 183-194

About this book

Introduction

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.

Keywords

Relational Mathematics Algebraic Topology Spatial Reasoning Kronecker Product of Relations Frames in Theoretical Computer Science as Topologies Aumann Contacts Proximity Nearness Simplicial Complexes Quantifier-free logic

Authors and affiliations

  • Gunther Schmidt
    • 1
  • Michael Winter
    • 2
  1. 1.Fakultät für InformatikUniversität der Bundeswehr MünchenNeubibergGermany
  2. 2.Department of Computer ScienceBrock UniversitySt. CatharinesCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74451-3
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74450-6
  • Online ISBN 978-3-319-74451-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site