Index Analysis : Approach Theory at Work

Resource Information

The work Index Analysis : Approach Theory at Work represents a distinct intellectual or artistic creation found in European University Institute. This resource is a combination of several types including: Work, Language Material, Books.

Label

Index Analysis : Approach Theory at Work

Title remainder

Approach Theory at Work

Statement of responsibility

by R. Lowen

Creator

• Lowen, R

Contributor

• SpringerLink (Online service)

Author

• Lowen, R

Subject

• Functional analysis
• Geometry
• Mathematics
• Ordered algebraic structures
• Probabilities
• Topology
• Algebra
• Approximation theory

Language

eng

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

Member of

• Springer Monographs in Mathematics,
• Springer eBooks, Mathematics and Statistics Collection

Image bit depth

0

Literary form

non fiction

Series statement

Springer Monographs in Mathematics,