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Cover: 9783319744506 | Relational Topology | Gunther Schmidt (u. a.) | Taschenbuch | xiv
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Relational Topology
Taschenbuch von Gunther Schmidt (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Gunther Schmidt arbeitete in der Komplexen Analysis, geriet aber als Mitarbeiter in die Ingenieurmathematik. Der in München sich entwickelnden Informatik half er früh mit Projekten und Vorlesungen zu Logik, Semantik, Übersetzerbau und Graphentheorie. Seine Arbeit über Relationen machte ihn zum vielfachen Herausgeber und Buchautor.
Zusammenfassung

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

Inhaltsverzeichnis
1.Introduction.- 2. Prerequisites.- 3. Products of Relations.- 4. Meet and Join as Relations.- 5. Applying Relations in Topology.- 6. Construction of Topologies.- 7. Closures and their Aumann Contacts.- 8. Proximity and Nearness.- 9. Frames.- 10. Simplicial Complexes.
Details
Erscheinungsjahr: 2018
Fachbereich: Geometrie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: xiv
194 S.
36 s/w Illustr.
68 farbige Illustr.
194 p. 104 illus.
68 illus. in color.
ISBN-13: 9783319744506
ISBN-10: 331974450X
Sprache: Englisch
Herstellernummer: 978-3-319-74450-6
Einband: Kartoniert / Broschiert
Autor: Schmidt, Gunther
Winter, Michael
Auflage: 1st edition 2018
Hersteller: Springer
Palgrave Macmillan
Springer International Publishing AG
Lecture Notes in Mathematics
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 12 mm
Von/Mit: Gunther Schmidt (u. a.)
Erscheinungsdatum: 02.06.2018
Gewicht: 0,324 kg
Artikel-ID: 111022103
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