000 | 03321nam a22005055i 4500 | ||
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001 | 978-3-540-46610-9 | ||
003 | DE-He213 | ||
005 | 20190213151745.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1991 gw | s |||| 0|eng d | ||
020 |
_a9783540466109 _9978-3-540-46610-9 |
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024 | 7 |
_a10.1007/BFb0089156 _2doi |
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_aPBP _2bicssc |
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_aMAT038000 _2bisacsh |
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_aPBP _2thema |
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_a514 _223 |
100 | 1 |
_aWicks, Keith R. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aFractals and Hyperspaces _h[electronic resource] / _cby Keith R. Wicks. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1991. |
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300 |
_aVIII, 172 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1492 |
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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 | _aTopology. | |
650 | 0 | _aGeometry. | |
650 | 0 | _aLogic, Symbolic and mathematical. | |
650 | 1 | 4 |
_aTopology. _0http://scigraph.springernature.com/things/product-market-codes/M28000 |
650 | 2 | 4 |
_aGeometry. _0http://scigraph.springernature.com/things/product-market-codes/M21006 |
650 | 2 | 4 |
_aMathematical Logic and Foundations. _0http://scigraph.springernature.com/things/product-market-codes/M24005 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662184684 |
776 | 0 | 8 |
_iPrinted edition: _z9783540549659 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1492 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0089156 |
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