000 03073nam a22005055i 4500
001 978-3-540-46610-9
003 DE-He213
005 20160624101823.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540466109
_9978-3-540-46610-9
024 7 _a10.1007/BFb0089156
_2doi
050 4 _aQA611-614.97
072 7 _aPBP
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514
_223
100 1 _aWicks, Keith R.
_eauthor.
245 1 0 _aFractals and Hyperspaces
_h[electronic resource] /
_cby Keith R. Wicks.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
300 _aVIII, 172 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1492
505 0 _aPreliminaries -- Nonstandard development of the vietoris topology -- Nonstandard development of the Hausdorff metric -- Hutchinson's invariant sets -- Views and fractal notions.
520 _aAddressed 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.
650 0 _aMathematics.
650 0 _aGeometry.
650 0 _aLogic, Symbolic and mathematical.
650 0 _aTopology.
650 1 4 _aMathematics.
650 2 4 _aTopology.
650 2 4 _aGeometry.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540549659
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1492
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0089156
942 _2EBK1424
_cEBK
999 _c30718
_d30718