Fractals and Hyperspaces (Record no. 30718)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03073nam a22005055i 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783540466109 |
| -- | 978-3-540-46610-9 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Wicks, Keith R. |
| 245 10 - TITLE STATEMENT | |
| Title | Fractals and Hyperspaces |
| Statement of responsibility, etc | by Keith R. Wicks. |
| 260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Berlin, Heidelberg : |
| Name of publisher | Springer Berlin Heidelberg, |
| Year of publication | 1991. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | VIII, 172 p. |
| Other physical details | online resource. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Preliminaries -- Nonstandard development of the vietoris topology -- Nonstandard development of the Hausdorff metric -- Hutchinson's invariant sets -- Views and fractal notions. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Logic, Symbolic and mathematical. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Topology. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Topology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematical Logic and Foundations. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/BFb0089156 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg, |
| -- | 1991. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0075-8434 ; |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK1424 | http://dx.doi.org/10.1007/BFb0089156 | E-BOOKS |