rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Index Analysis
    sub title: Approach Theory at Work
  name:
    name part: Lowen, R.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxk
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXI, 466 p. 58 illus. online resource.
  abstract: 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.
  table of 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.
  note: by R. Lowen.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Ordered algebraic structures
  subject:
    topic: Approximation theory
  subject:
    topic: Functional analysis
  subject:
    topic: Geometry
  subject:
    topic: Probabilities
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Order, Lattices, Ordered Algebraic Structures
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Functional Analysis
  subject:
    topic: Topology
  subject:
    topic: Probability Theory and Stochastic Processes
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9781447164852
  identifier: http://dx.doi.org/10.1007/978-1-4471-6485-2
  record info:
    record creation date: 150105
    record change date: 20151030001313.0
    record identifier: 978-1-4471-6485-2