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Cover: 9783319744506 | Relational Topology | Michael Winter (u. a.) | Taschenbuch | Paperback
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Relational Topology
Taschenbuch von Michael Winter (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.
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
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: Winter, Michael
Schmidt, Gunther
Auflage: 1st edition 2018
Hersteller: Springer International Publishing
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: Michael Winter (u. a.)
Erscheinungsdatum: 02.06.2018
Gewicht: 0,324 kg
Artikel-ID: 111022103
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
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: Winter, Michael
Schmidt, Gunther
Auflage: 1st edition 2018
Hersteller: Springer International Publishing
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: Michael Winter (u. a.)
Erscheinungsdatum: 02.06.2018
Gewicht: 0,324 kg
Artikel-ID: 111022103
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