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商品描述
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.
商品描述(中文翻譯)
本書介紹並發展了新的代數方法，以處理關係，這些關係通常被視為布林矩陣，並將其應用於拓撲學。儘管這些對象反映了數學、數值分析、統計學、工程學等領域中出現的矩陣，但用於處理它們的方法卻鮮為人知。除了其純粹的拓撲應用外，本書還詳細說明了這些技術如何成功應用於空間推理和計算機科學的邏輯。
拓撲學家將會發現幾個熟悉的概念以簡潔且可代數操作的形式呈現，這種形式比通常的表達方式更加緊湊，但通過表示的關係進行可視化，因此易於理解。這種方法還提供了使用證明助手處理拓撲問題的可能性。
