Relational Topology

• Main Authors: Schmidt, Gunther (Author, http://id.loc.gov/vocabulary/relators/aut), Winter, Michael (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2208
• Subjects: Topology.; Mathematical logic.; Category theory (Mathematics).; Homological algebra.; Algebra.; Computer science-Mathematics.; Computer mathematics.; Discrete mathematics.; Mathematical Logic and Foundations.; Category Theory, Homological Algebra.; General Algebraic Systems.; Mathematical Applications in Computer Science.; Discrete Mathematics.

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...

Table of Contents:

• 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.