Index analysis : approach theory at work / R. Lowen.
By: Lowen, R.
Material type: TextSeries: Springer monographs in mathematics.Publisher: London : SpringerVerlag, 2015Description: xxi, 466 p. : illustrations ; 25 cm.ISBN: 9781447164845.Subject(s): Index theory (Mathematics)  Topological spacesDDC classification: 514.74Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

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ISI Library, Kolkata

514.74 L917 (Browse shelf)  Available  136640 
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514.74 L529 Simulating Hamiltonian dynamics  514.74 L529 Simulating Hamiltonian dynamics  514.74 L849 Index theory for symplectic paths with applications  514.74 L917 Index analysis :  514.74 M139 Introduction to symplectic topology  514.74 M364 Hamiltonian reduction by stages  514.74 M419 Fractual functions,fractual surfaces,and wavelets 
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.
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