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020 _a9783319744513
_9978-3-319-74451-3
024 7 _a10.1007/978-3-319-74451-3
_2doi
040 _cCUS
050 4 _aQA611-614.97
072 7 _aPBP
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBP
_2thema
082 0 4 _a514
_223
100 1 _aSchmidt, Gunther.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aRelational Topology
_h[electronic resource] /
_cby Gunther Schmidt, Michael Winter.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXIV, 194 p. 104 illus., 68 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2208
505 0 _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.
520 _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.
650 0 _aTopology.
650 0 _aMathematical logic.
650 0 _aCategory theory (Mathematics).
650 0 _aHomological algebra.
650 0 _aAlgebra.
650 0 _aComputer science—Mathematics.
650 0 _aComputer mathematics.
650 0 _aDiscrete mathematics.
650 1 4 _aTopology.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M28000
650 2 4 _aMathematical Logic and Foundations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M24005
650 2 4 _aCategory Theory, Homological Algebra.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11035
650 2 4 _aGeneral Algebraic Systems.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
650 2 4 _aMathematical Applications in Computer Science.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M13110
650 2 4 _aDiscrete Mathematics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M29000
700 1 _aWinter, Michael.
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2208
856 4 0 _uhttps://doi.org/10.1007/978-3-319-74451-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
942 _cEBK
999 _c206808
_d206808