About this Volume
Edited by: Frédéric Mynard and Elliott Pearl
2009: Volume: 486
ISBNs: 978-0-8218-4279-9 (print); 978-0-8218-8165-1 (online)
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Graduate students and research mathematicians interested in topology, geometry, analysis, and the foundations of mathematics.
Table of Contents
- Robert Lowen, Mark Sioen and Stijn Verwulgen – Categorical topology
- H. Lamar Bentley, Eva Colebunders and Eva Vandersmissen – A convenient setting for completions and function spaces
- Anna Di Concilio – Proximity: a powerful tool in extension theory, function spaces, hyperspaces, Boolean algebras and point-free geometry
- Szymon Dolecki – An initiation into convergence theory
- Marcel Erné – Closure
- Hans-Peter A. Künzi – An introduction to quasi-uniform spaces
- Robert Lowen and Christophe Van Olmen – Approach theory
- Gerhard Preuß – Semiuniform convergence spaces and filter spaces