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: Spaces of Continuous Functions
  name:
    name part: Groenewegen, G.L.M.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: van Rooij, A.C.M.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: fr
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: IX, 173 p. 23 illus. online resource.
  abstract: The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given. Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem. The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
  table of contents: Topological Preliminaries -- Metrizable Compact Spaces -- The Stone-Weierstrass Theorem -- Weak Topologies. The Alaoglu Theorem -- Riesz Spaces -- Yosida’s Representation Theorem -- The Stone-Čech compactification -- Evaluations -- C(X) determines X -- The Riesz Representation Theorem -- Banach Algebras -- Other Scalars.
  note: by G.L.M. Groenewegen, A.C.M. van Rooij.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Measure theory
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Measure and Integration
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Atlantis Studies in Mathematics, 4
  identifier: 9789462392014
  identifier: http://dx.doi.org/10.2991/978-94-6239-201-4
  record info:
    record creation date: 160617
    record change date: 20160617065108.0
    record identifier: 978-94-6239-201-4