Measure, Topology, and Fractal Geometry
Measure, Topology, and Fractal Geometry
复制标题
DOI：
10.5860/choice.28-5119
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
G. A. Edgar
中科院分区：
文献类型：
--
作者：
G. A. Edgar
* 桥梁差距之间的传统书籍拓扑/分析和更专门的论文分形几何 * 包含大量的例子，练习，和插图 * 理想的课堂使用与一个独立的和仔细的介绍对于第二版这一高度重视的教科书，杰拉尔德埃德加作出了许多补充和修改，试图提供一个更清晰，更集中的论述。最重要的补充是增加了对填充测度的强调，因此现在它经常被视为与豪斯多夫测度相同。在第三章中，拓扑维被重新排列，因此覆盖维是主要的，归纳维是变体。一个“减少覆盖类”的概念被引入，以帮助证明方法I或方法II的措施。自1990年以来影响这些基本主题的研究成果已被考虑在内。增加了一些例子，包括巴恩斯利叶和朱莉娅集，大部分图形都重新绘制。来自第一版的评论：“..关于计算机使用递归或迭代算法绘制的美丽的数学对象的书籍、文章和电视节目如洪水般泛滥，曼德尔布罗特将其命名为分形。杰拉尔德埃德加的书是一个重要的补充，这洪水。根据课程给予有才华的高中学生在俄亥俄州大学于1988年，这是，事实上，一个先进的本科教科书数学的分形几何，治疗等主题的度量空间，测度论，维数理论，甚至一些代数拓扑.这本书还包含了许多关于分形的很好的插图。“-数学教学“这本书可以推荐给学生谁认真想知道的数学基础的分形，并向讲师谁想要说明一个标准的过程中度量拓扑有趣的例子。- Christoph Bandt，Mathematical Reviews.不仅适合希望从一开始就学习分形几何的数学学生，而且适合对该主题感兴趣的计算机科学学生。[For这样的学生]作者给出了要求的主题从度量拓扑和测度理论在一个初级的水平。这本书写得很清楚，里面有很多应该做的练习。- H.Haase，Zentralblatt
* Bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry * Contains plenty of examples, exercises, and illustrations * Ideal for classroom use with a self-contained and careful presentation 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