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: Metric Spaces
  name:
    name part: Searcóid, Mícheál Ó.
    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: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 304 p. 102 illus. online resource.
  abstract: The abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease. The book goes on to provide a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length. Other features include: end-of-chapter summaries and numerous exercises to reinforce what has been learnt; extensive cross-referencing to help the reader follow arguments; a Cumulative Reference Chart, showing the dependencies throughout the book on a section-by-section basis as an aid to course design. The book is designed for third- and fourth-year undergraduates and beginning graduates. Readers should have some practical knowledge of differential and integral calculus and have completed a first course in real analysis. With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications.
  table of contents: Metrics -- Distance -- Boundary -- Open, Closed and Dense Subsets -- Balls -- Convergence -- Bounds -- Continuity -- Uniform Continuity -- Completeness -- Connectedness -- Compactness -- Equivalence.
  note: by Mícheál Ó Searcóid.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Functional analysis
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Functional Analysis
  subject:
    topic: Topology
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Undergraduate Mathematics Series
  identifier: 9781846286278
  identifier: http://dx.doi.org/10.1007/978-1-84628-627-8
  record info:
    record creation date: 100301
    record change date: 20151204140650.0
    record identifier: 978-1-84628-627-8