Relational Topology - Gunther Schmidt

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Résumé :
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.

Biographie:
Gunther Schmidt arbeitete in der Komplexen Analysis, geriet aber als Mitarbeiter in die Ingenieurmathematik. Der in M?nchen sich entwickelnden Informatik half er fr?h mit Projekten und Vorlesungen zu Logik, Semantik, ?bersetzerbau und Graphentheorie. Seine Arbeit ?ber Relationen machte ihn zum vielfachen Herausgeber und Buchautor. ...

Sommaire:
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.