02863nam a2200493 i 4500991003636179707536m o d cr |n|||||||||190408s2018 sz ob 001 0 eng d3319744518(electronic bk.)9783319744513(electronic bk.)331974450X978331974450610.1007/978-3-319-74451-3doib14363896-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng51423AMS 54-01LC QA611Schmidt, Günther502593Relational topology[e-book] /by Gunther Schmidt, Michael WinterCham :Springer,20181 online resource (xiv, 198 p. 104 illus., 64 illus. in colortexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,0075-8434 ;22081.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 ComplexesThis 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 assistantsCategories (Mathematics)Algebra, HomologicalAlgebraComputer scienceMathematicsLogic, Symbolic and mathematicalTopologyWinter, Michaelauthorhttp://id.loc.gov/vocabulary/relators/aut566406Printed edition:9783319744506An electronic book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-3-319-74451-3.b1436389603-03-2208-04-19991003636179707536Relational topology1524079UNISALENTOle01308-04-19m@ -engsz 00