Index analysis [electronic resource] : approach theory at work / R. Lowen.
2015
QA614.92
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Title
Index analysis [electronic resource] : approach theory at work / R. Lowen.
Author
Lowen, R. (Robert), author.
ISBN
9781447164852 electronic book
1447164857 electronic book
9781447164845
1447164857 electronic book
9781447164845
Published
London : Springer, 2015.
Language
English
Description
1 online resource (xxi, 466 pages) : illustrations.
Item Number
10.1007/978-1-4471-6485-2 doi
Call Number
QA614.92
Dewey Decimal Classification
514/.74
Summary
A 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed January 29, 2015).
Series
Springer monographs in mathematics.
Available in Other Form
Print version: 9781447164845
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Table of Contents
Approach spaces
Topological and metric approach spaces
Approach invariants
Index analysis
Uniform gauge spaces
Extensions of spaces and morphisms
Approach theory meets Topology
Approach theory meets Functional analysis
Approach theory meets Probability
Approach theory meets Hyperspaces
Approach theory meets DCPO?s and Domains
Categorical considerations.
Topological and metric approach spaces
Approach invariants
Index analysis
Uniform gauge spaces
Extensions of spaces and morphisms
Approach theory meets Topology
Approach theory meets Functional analysis
Approach theory meets Probability
Approach theory meets Hyperspaces
Approach theory meets DCPO?s and Domains
Categorical considerations.