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

Format:

Book

Author/Creator:

Lowen, R., Author.

Series:

Springer Monographs in Mathematics, 1439-7382

Language:

English

Subjects (All):

Geometry.

Algebra.

Ordered algebraic structures.

Approximation theory.

Functional analysis.

Topology.

Probabilities.

Order, Lattices, Ordered Algebraic Structures.

Approximations and Expansions.

Functional Analysis.

Probability Theory and Stochastic Processes.

Local Subjects:

Geometry.

Order, Lattices, Ordered Algebraic Structures.

Approximations and Expansions.

Functional Analysis.

Topology.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (477 p.)

Edition:

1st ed. 2015.

Place of Publication:

London : Springer London : Imprint: Springer, 2015.

Language Note:

English

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.

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-4471-6485-7

OCLC:

899495713