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＜電子ブック＞
Relational Topology / by Gunther Schmidt, Michael Winter
(Lecture Notes in Mathematics. ISSN:16179692 ; 2208)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	XIV, 194 p. 104 illus., 68 illus. in color : online resource
著者標目	*Schmidt, Gunther author Winter, Michael author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Mathematical logic LCSH:Algebra, Homological LCSH:Universal algebra LCSH:Computer science—Mathematics LCSH:Discrete mathematics FREE:Topology FREE:Mathematical Logic and Foundations FREE:Category Theory, Homological Algebra FREE:General Algebraic Systems FREE:Mathematical Applications in Computer Science FREE:Discrete Mathematics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-74451-3

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