000 | 03623nam a22006015i 4500 | ||
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001 | 978-3-319-74451-3 | ||
003 | DE-He213 | ||
005 | 20200812132912.0 | ||
007 | cr nn 008mamaa | ||
008 | 180531s2018 gw | s |||| 0|eng d | ||
020 |
_a9783319744513 _9978-3-319-74451-3 |
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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 |
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072 | 7 |
_aPBP _2thema |
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |
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