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Springer Monographs in Mathematics Ser.: Index Analysis : Approach Theory at Work by R. Lowen (2015, Hardcover)
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About this product
Product Identifiers
PublisherSpringer London, The Limited
ISBN-101447164849
ISBN-139781447164845
eBay Product ID (ePID)201617807
Product Key Features
Number of PagesXxi, 466 Pages
Publication NameIndex Analysis : Approach Theory at Work
LanguageEnglish
SubjectAlgebra / Abstract, Functional Analysis, Geometry / General, General, Mathematical Analysis
Publication Year2015
TypeTextbook
AuthorR. Lowen
Subject AreaMathematics
SeriesSpringer Monographs in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight300.3 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2014-942538
Dewey Edition23
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal514.325
Table Of ContentApproach 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.
SynopsisApproach 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., 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.
LC Classification NumberQA440-699
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