Relational Topology

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, enginee

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Gunther Schmidt Michael Winter

Relational Topology

Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg

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More information about this series at http://www.springer.com/series/304

Gunther Schmidt • Michael Winter

Relational Topology

123

Gunther Schmidt FakultRat fRur Informatik UniversitRat der Bundeswehr MRunchen Neubiberg, Germany

Michael Winter Department of Computer Science Brock University St. Catharines, Ontario, Canada

ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-74450-6 ISBN 978-3-319-74451-3 (eBook) https://doi.org/10.1007/978-3-319-74451-3 Library of Congress Control Number: 2018942705 Mathematics Subject Classification (2010): 54-XX, 03E20, 54E05, 54E17, 97E60 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Over the years, the authors have encountered a multitude of topics that are ultimately related to general topology and the logics of spatial reasoning. On the other hand, they have long been working on and with relational methods in fields around computer science. Finally, programming was their daily lecturing task. They became increasingly unsatisfied with the many—but slightly diverging—approaches to the topics mentioned and decided to work on a unifying presentation. Yet another stimulus was the id