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180604 ||| eng |
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|a 9783319744513
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| 100 |
1 |
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|a Schmidt, Gunther
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| 245 |
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|a Relational Topology
|h Elektronische Ressource
|c by Gunther Schmidt, Michael Winter
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| 250 |
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|a 1st ed. 2018
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| 260 |
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|a Cham
|b Springer International Publishing
|c 2018, 2018
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| 300 |
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|a XIV, 194 p. 104 illus., 68 illus. in color
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Computer science—Mathematics
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| 653 |
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|a General Algebraic Systems
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| 653 |
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|a Mathematical Applications in Computer Science
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| 653 |
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|a Discrete Mathematics
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| 653 |
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|a Topology
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| 653 |
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|a Homological algebra
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| 653 |
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|a Mathematical logic
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| 653 |
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|a Mathematical Logic and Foundations
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| 653 |
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|a Topology
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| 653 |
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|a Algebra
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| 653 |
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|a Computer mathematics
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| 653 |
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|a Category Theory, Homological Algebra
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| 653 |
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|a Discrete mathematics
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| 653 |
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|a Category theory (Mathematics)
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| 700 |
1 |
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|a Winter, Michael
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Lecture Notes in Mathematics
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-319-74451-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 514
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| 520 |
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|a 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
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