000 03904nam a22005055i 4500
001 978-0-387-74749-1
003 DE-He213
005 20161121231208.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387747491
_9978-0-387-74749-1
024 7 _a10.1007/978-0-387-74749-1
_2doi
050 4 _aQA611-614.97
072 7 _aPBP
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514
_223
245 1 0 _aMeasure, Topology, and Fractal Geometry
_h[electronic resource] /
_cedited by Gerald Edgar.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aXVI, 272 p. 169 illus., 20 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUndergraduate Texts in Mathematics,
_x0172-6056
505 0 _aFractal Examples -- Metric Topology -- Topological Dimension -- Self-Similarity -- Measure Theory -- Fractal Dimension -- Additional Topics.
520 _aFor the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so that now it is often treated on a par with the Hausdorff measure. The topological dimensions were rearranged for Chapter 3, so that the covering dimension is the major one, and the inductive dimensions are the variants. A "reduced cover class" notion was introduced to help in proofs for Method I or Method II measures. Research results since 1990 that affect these elementary topics have been taken into account. Some examples have been added, including Barnsley leaf and Julia set, and most of the figures have been re-drawn. From reviews of the First Edition: "...there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high-school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals..." - Mathematics Teaching "The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples." - Christoph Bandt, Mathematical Reviews "...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. [For such students] the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out." - H.Haase, Zentralblatt.
650 0 _aMathematics.
650 0 _aMeasure theory.
650 0 _aFunctions of real variables.
650 0 _aGeometry.
650 0 _aTopology.
650 1 4 _aMathematics.
650 2 4 _aTopology.
650 2 4 _aReal Functions.
650 2 4 _aGeometry.
650 2 4 _aMeasure and Integration.
700 1 _aEdgar, Gerald.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387747484
830 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-74749-1
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509959
_d509959