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: Fractals and Universal Spaces in Dimension Theory
  name:
    name part: Lipscomb, Stephen.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 242 p. 91 illus., 15 illus. in color. online resource.
  abstract: For metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods — the classical (separable metric) and the modern (not necessarily separable metric). While the classical theory is now well documented in several books, this is the first book to unify the modern theory (1960 – 2007). Like the classical theory, the modern theory fundamentally involves the unit interval. By the 1970s, the author of this monograph generalized Cantor’s 1883 construction (identify adjacent-endpoints in Cantor’s set) of the unit interval, obtaining — for any given weight — a one-dimensional metric space that contains rationals and irrationals as counterparts to those in the unit interval. Following the development of fractal geometry during the 1980s, these new spaces turned out to be the first examples of attractors of infinite iterated function systems — “generalized fractals.” The use of graphics to illustrate the fractal view of these spaces is a unique feature of this monograph. In addition, this book provides historical context for related research that includes imbedding theorems, graph theory, and closed imbeddings. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. It can also serve as a text for graduate seminars or self-study — the interested reader will find many relevant open problems that will motivate further research into these topics.
  table of contents: Construction of = -- Self-Similarity and for Finite -- No-Carry Property of -- Imbedding in Hilbert Space -- Infinite IFS with Attractor -- Dimension Zero -- Decompositions -- The Imbedding Theorem -- Minimal-Exponent Question -- The Imbedding Theorem -- 1992#x2013;2007 -Related Research -- Isotopy Moves into 3-Space -- From 2-Web IFS to 2-Simplex IFS 2-Space and the 1-Sphere -- From 3-Web IFS to 3-Simplex IFS 3-Space and the 2-Sphere.
  note: by Stephen Lipscomb.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functions of complex variables
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: Topology
  subject:
    topic: Analysis
  subject:
    topic: Functions of a Complex Variable
  subject:
    topic: Dynamical Systems and Ergodic Theory
  classification: QA611-614.97
  classification: 514
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9780387854946
  identifier: http://dx.doi.org/10.1007/978-0-387-85494-6
  record info:
    record creation date: 110406
    record change date: 20151204140809.0
    record identifier: 978-0-387-85494-6