Relational Topology [electronic resource] / by Gunther Schmidt, Michael Winter.
Material type: TextSeries: Lecture Notes in Mathematics ; 2208Publisher: Cham : Springer International Publishing : Imprint: Springer, 2018Edition: 1st ed. 2018Description: XIV, 194 p. 104 illus., 68 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319744513Subject(s): Topology | Mathematical logic | Category theory (Mathematics) | Homological algebra | Algebra | Computer science—Mathematics | Computer mathematics | Discrete mathematics | Topology | Mathematical Logic and Foundations | Category Theory, Homological Algebra | General Algebraic Systems | Mathematical Applications in Computer Science | Discrete MathematicsDDC classification: 514 LOC classification: QA611-614.97Online resources: Click here to access onlineItem type | Current library | Call number | Status | Date due | Barcode | Item holds |
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e-Books | Central Library, Sikkim University | 514 (Browse shelf(Opens below)) | Not for loan | E-3046 |
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513.83 SIM/I Introduction to topology and modern analysis/ | 513.9.CI SIN/M Mental ability test general intelligence test/reasoning ability test/ | 514 Introduction to Topology | 514 Relational Topology | 514 ARM/ Basic topology/ | 514 ARM/ Basic topology/ | 514 ARM/ Basic topology/ |
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.
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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