Buch, Englisch, Band 2208, 194 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 2208, 194 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-319-74450-6
Verlag: Springer International Publishing
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
- Mathematik | Informatik Mathematik Topologie
Weitere Infos & Material
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.
