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.
