Relational Topology, 1st ed. 2018 Lecture Notes in Mathematics Series, Vol. 2208

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.

Introduces and develops an algebraic treatment of Boolean matrices

Applies the methods to give an algebraic treatment of point set topology

Offers a framework for handling topological problems using theorem provers

Includes nearly 100 diagrams of relations presented as matrices