Overview
- Provides a self-contained introduction to approach theory and index analysis
- Presents applications to topology, functional analysis, probability, hyperspaces and domains
- Includes a thorough analysis of the categorical setup of the theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The featured review of the AMS describes the author’s earlier work in the field of approach spaces as, ‘A landmark in the history of general topology’. In this book, the author has expanded this study further and taken it in a new and exciting direction.
The number of conceptually and technically different systems which characterize approach spaces is increased and moreover their uniform counterpart, uniform gauge spaces, is put into the picture. An extensive study of completions, both for approach spaces and for uniform gauge spaces, as well as compactifications for approach spaces is performed. A paradigm shift is created by the new concept of index analysis.
Making use of the rich intrinsic quantitative information present in approach structures, a technique is developed whereby indices are defined that measure the extent to which properties hold, and theorems become inequalities involving indices; therefore vastly extending the realm of applicability of many classical results. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory. Finally a comprehensive analysis is made concerning the categorical aspects of the theory and its links with other topological categories.
Index Analysis will be useful for mathematicians working in category theory, topology, probability and statistics, functional analysis, and theoretical computer science.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Index Analysis
Book Subtitle: Approach Theory at Work
Authors: R. Lowen
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-1-4471-6485-2
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2015
Hardcover ISBN: 978-1-4471-6484-5Published: 19 January 2015
Softcover ISBN: 978-1-4471-7266-6Published: 24 September 2016
eBook ISBN: 978-1-4471-6485-2Published: 06 January 2015
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXI, 466
Number of Illustrations: 58 b/w illustrations
Topics: Geometry, Order, Lattices, Ordered Algebraic Structures, Approximations and Expansions, Functional Analysis, Topology, Probability Theory and Stochastic Processes