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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Michael Winter is the author of The Big Why (winner of the Drummer General's Award and nominated for Ontario's Trillium Book Award and the Atlantic Book Awards Thomas Head Raddall Fiction Prize), This All Happened (winner of the Winterset Award and nominated for the Rogers Writers' Trust Fiction Prize), the short-story collection One Last Good Look, and more recently the novels The Architects Are Here and The Death of Donna Whalen.

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