Fractals and Universal Spaces in Dimension Theory [electronic resource] / by Stephen Lipscomb.

By:

Lipscomb, Stephen [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Springer Monographs in MathematicsPublisher: New York, NY : Springer New York, 2009Description: XVIII, 242 p. 91 illus., 15 illus. in color. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9780387854946

Subject(s):

Additional physical formats: Printed edition:: No titleDDC classification:

514 23

LOC classification:

QA611-614.97

Online resources:

Click here to access online

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.

In: Springer eBooksSummary: 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.

Holdings ( 1 )
Title notes ( 2 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
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Total holds: 0

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.