TY  - BOOK
AU  - Schmidt,Gunther
AU  - Winter,Michael
TI  - Relational Topology
T2  - Lecture Notes in Mathematics,
SN  - 9783319744513
AV  - QA611-614.97 
U1  - 514 23
PY  - 2018///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Topology
KW  - Mathematical logic
KW  - Category theory (Mathematics)
KW  - Homological algebra
KW  - Algebra
KW  - Computer science—Mathematics
KW  - Computer mathematics
KW  - Discrete mathematics
KW  - Mathematical Logic and Foundations
KW  - Category Theory, Homological Algebra
KW  - General Algebraic Systems
KW  - Mathematical Applications in Computer Science
KW  - Discrete Mathematics
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-74451-3
ER  -