03821nam a22004695i 4500 978-0-387-74749-1 DE-He213 20260521091950.0 cr nn 008mamaa 100301s2008 xxu| s |||| 0|eng d 9780387747491 99780387747491 10.1007/978-0-387-74749-1 doi CICY 514 23 Edgar, Gerald. editor. Measure, Topology, and Fractal Geometry [recurso electrónico] / edited by Gerald Edgar. New York, NY : Springer New York, 2008. XVI, 272 p. 169 illus., 20 illus. in color. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Undergraduate Texts in Mathematics, 0172-6056 Fractal Examples -- Metric Topology -- Topological Dimension -- Self-Similarity -- Measure Theory -- Fractal Dimension -- Additional Topics. For 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 MATHEMATICS. GEOMETRY. TOPOLOGY. MATHEMATICS. TOPOLOGY. REAL FUNCTIONS. GEOMETRY. MEASURE AND INTEGRATION. SpringerLink (Online service) Springer eBooks Printed edition: 9780387747484 Undergraduate Texts in Mathematics, 0172-6056 http://dx.doi.org/10.1007/978-0-387-74749-1 Ver el texto completo en las instalaciones del CICY ddc ER 34566 34566 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 514 2025-07-10 08:40:21 2025-07-10 ER