Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorWicks, Keith R. author
TitleFractals and Hyperspaces [electronic resource] / by Keith R. Wicks
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1991
Connect tohttp://dx.doi.org/10.1007/BFb0089156
Descript VIII, 172 p. online resource

SUMMARY

Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included


CONTENT

Preliminaries -- Nonstandard development of the vietoris topology -- Nonstandard development of the Hausdorff metric -- Hutchinson's invariant sets -- Views and fractal notions


Mathematics Geometry Mathematical logic Topology Mathematics Topology Geometry Mathematical Logic and Foundations



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram