Relational topology
- 作者： Schmidt, Gunther, author.
- 其他作者：
- 其他題名：
- Lecture notes in mathematics ;
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Lecture notes in mathematics,2208
- 主題： Topology. , Mathematics. , Topology. , Mathematical Logic and Foundations. , Category Theory, Homological Algebra. , General Algebraic Systems. , Mathematical Applications in Computer Science. , Discrete Mathematics.
- ISBN： 9783319744513 (electronic bk.) 、 9783319744506 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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.
- 摘要註: 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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讀者標籤：
- 系統號： 005430315 | 機讀編目格式
館藏資訊
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.