04070nam 22007575 450 99646654330331620200704121212.03-319-74451-810.1007/978-3-319-74451-3(DE-He213)978-3-319-74451-3(MiAaPQ)EBC6301615(PPN)227403258(EXLCZ)99410000000424359420180531d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierRelational Topology[electronic resource] /by Gunther Schmidt, Michael Winter1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XIV, 194 p. 104 illus., 68 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;22083-319-74450-X 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.Lecture Notes in Mathematics,0075-8434 ;2208TopologyMathematical logicCategory theory (Mathematics)Homological algebraAlgebraComputer science—MathematicsComputer mathematicsDiscrete mathematicsTopologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28000Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035General Algebraic Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M1106XMathematical Applications in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/M13110Discrete Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M29000Topology.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 Mathematics.514Schmidt Guntherauthttp://id.loc.gov/vocabulary/relators/aut502593Winter Michaelauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996466543303316Relational Topology2102302UNISA