Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Normal view MARC view ISBD view

Index analysis : approach theory at work / R. Lowen.

By: Lowen, R.
Material type: TextTextSeries: Springer monographs in mathematics.Publisher: London : Springer-Verlag, 2015Description: xxi, 466 p. : illustrations ; 25 cm.ISBN: 9781447164845.Subject(s): Index theory (Mathematics) | Topological spacesDDC classification: 514.74
Contents:
1. Approach spaces -- 2. Topological and metric approach spaces -- 3. Approach invariants -- 4. Index analysis -- 5. Uniform gauge spaces -- 6. Extensions of spaces and morphisms -- 7. Approach theory meets Topology -- 8. Approach theory meets Functional analysis -- 9. Approach theory meets Probability -- 10. Approach theory meets Hyperspaces -- 11. Approach theory meets DCPO?s and Domains -- 12. Categorical considerations -- Appendixes -- References -- Index.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
514.74 L917 (Browse shelf) Available 136640
Total holds: 0

Includes bibliographical references and index.

1. Approach spaces --
2. Topological and metric approach spaces --
3. Approach invariants --
4. Index analysis --
5. Uniform gauge spaces --
6. Extensions of spaces and morphisms --
7. Approach theory meets Topology --
8. Approach theory meets Functional analysis --
9. Approach theory meets Probability --
10. Approach theory meets Hyperspaces --
11. Approach theory meets DCPO?s and Domains --
12. Categorical considerations --
Appendixes --
References --
Index.

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.

There are no comments for this item.

Log in to your account to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in


Visitor Counter