LEADER 03156nam 2200601 450 001 996466755103316 005 20220910123405.0 010 $a3-540-46610-X 024 7 $a10.1007/BFb0089156 035 $a(CKB)1000000000437091 035 $a(SSID)ssj0000323302 035 $a(PQKBManifestationID)12064857 035 $a(PQKBTitleCode)TC0000323302 035 $a(PQKBWorkID)10299285 035 $a(PQKB)11617585 035 $a(DE-He213)978-3-540-46610-9 035 $a(MiAaPQ)EBC5594734 035 $a(Au-PeEL)EBL5594734 035 $a(OCoLC)1076257117 035 $a(MiAaPQ)EBC6841900 035 $a(Au-PeEL)EBL6841900 035 $a(PPN)155226827 035 $a(EXLCZ)991000000000437091 100 $a20220910d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFractals and hyperspaces /$fKeith R. Wicks 205 $a1st ed. 1991. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1991] 210 4$dİ1991 215 $a1 online resource (VIII, 172 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1492 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54965-X 327 $aPreliminaries -- Nonstandard development of the vietoris topology -- Nonstandard development of the Hausdorff metric -- Hutchinson's invariant sets -- Views and fractal notions. 330 $aAddressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1492 606 $aFractals 606 $aHyperspace 615 0$aFractals. 615 0$aHyperspace. 676 $a514.74 700 $aWicks$b Keith R.$f1962-$059912 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466755103316 996 $aFractals and hyperspaces$9383038 997 $aUNISA