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Relational topology

Schmidt, Gunther.

Relational topology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Relational topologyby Gunther Schmidt, Michael Winter.
Author:	Schmidt, Gunther.
other author:	Winter, Michael.
Published:	Cham :Springer International Publishing :2018.
Description:	xiv, 194 p. :digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Topology.
Online resource:	http://dx.doi.org/10.1007/978-3-319-74451-3
ISBN:	9783319744513$q(electronic bk.)

Relational topology
Schmidt, Gunther.

Relational topology[electronic resource] /by Gunther Schmidt, Michael Winter. - Cham :Springer International Publishing :2018. - xiv, 194 p. :digital ;24 cm. - Lecture notes in mathematics,22080075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783319744513$q(electronic bk.)

Standard No.: 10.1007/978-3-319-74451-3doiSubjects--Topical Terms:

185965
Topology.

LC Class. No.: QA611 / .S365 2018

Dewey Class. No.: 514

Relational topology
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a General Algebraic Systems. $3 275666
650 2 4 $a Mathematical Applications in Computer Science. $3 530811
650 2 4 $a Discrete Mathematics. $3 524738
700 1 $a Winter, Michael. $3 279202
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