LEADER 04083nam  22007695  450 
001 9910300118803321
005 20200704121212.0
010   $a3-319-74451-8
024 7 $a10.1007/978-3-319-74451-3
035   $a(DE-He213)978-3-319-74451-3
035   $a(MiAaPQ)EBC6301615
035   $a(PPN)227403258
035   $a(CKB)4100000004243594
035   $a(EXLCZ)994100000004243594
100   $a20180531d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRelational Topology /$fby Gunther Schmidt, Michael Winter
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XIV, 194 p. 104 illus., 68 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2208
311   $a3-319-74450-X 
327   $a1.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.
330   $aThis book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2208
606   $aTopology
606   $aMathematical logic
606   $aCategory theory (Mathematics)
606   $aHomological algebra
606   $aAlgebra
606   $aComputer science?Mathematics
606   $aComputer mathematics
606   $aDiscrete mathematics
606   $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035
606   $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
606   $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110
606   $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000
615  0$aTopology.
615  0$aMathematical logic.
615  0$aCategory theory (Mathematics).
615  0$aHomological algebra.
615  0$aAlgebra.
615  0$aComputer science?Mathematics.
615  0$aComputer mathematics.
615  0$aDiscrete mathematics.
615 14$aTopology.
615 24$aMathematical Logic and Foundations.
615 24$aCategory Theory, Homological Algebra.
615 24$aGeneral Algebraic Systems.
615 24$aMathematical Applications in Computer Science.
615 24$aDiscrete Mathematics.
676   $a514
700   $aSchmidt$b Gunther$4aut$4http://id.loc.gov/vocabulary/relators/aut$0502593
702   $aWinter$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300118803321
996   $aRelational Topology$92102302
997   $aUNINA