This book, "Measure, Topology, and Fractal Geometry" by Gerald Edgar, is an undergraduate-level text that delves into the mathematical concepts of fractal geometry. The author, a professor at The Ohio State University, aims to provide a rigorous yet accessible introduction to the subject, suitable for students with a background in calculus and basic set theory. The book covers fundamental topics such as metric topology, topological dimension, self-similarity, and measure theory, with a focus on fractal dimensions. Key features of the book include: - **Fractal Examples**: Introduces various fractal sets and their properties. - **Metric Topology**: Discusses the necessary background in metric spaces and topological concepts. - **Topological Dimension**: Explains different types of dimensions, including covering dimension and inductive dimensions. - **Self-Similarity**: Explores the concept of self-similarity and its applications. - **Measure Theory**: Covers Lebesgue measure and its role in fractal geometry. - **Fractal Dimension**: Introduces the Hausdorff measure and dimension, and discusses various methods for calculating fractal dimensions. - **Additional Topics**: Includes sections on deconstruction and other advanced topics. The book is structured into several chapters, each focusing on a specific aspect of fractal geometry. It also includes an appendix with definitions, notation, examples, and references. The second edition, published in 2007, includes updates and changes based on feedback from readers and recent research, such as increased emphasis on packing measure and new examples like the Barnsley leaf and Julia set.This book, "Measure, Topology, and Fractal Geometry" by Gerald Edgar, is an undergraduate-level text that delves into the mathematical concepts of fractal geometry. The author, a professor at The Ohio State University, aims to provide a rigorous yet accessible introduction to the subject, suitable for students with a background in calculus and basic set theory. The book covers fundamental topics such as metric topology, topological dimension, self-similarity, and measure theory, with a focus on fractal dimensions. Key features of the book include: - **Fractal Examples**: Introduces various fractal sets and their properties. - **Metric Topology**: Discusses the necessary background in metric spaces and topological concepts. - **Topological Dimension**: Explains different types of dimensions, including covering dimension and inductive dimensions. - **Self-Similarity**: Explores the concept of self-similarity and its applications. - **Measure Theory**: Covers Lebesgue measure and its role in fractal geometry. - **Fractal Dimension**: Introduces the Hausdorff measure and dimension, and discusses various methods for calculating fractal dimensions. - **Additional Topics**: Includes sections on deconstruction and other advanced topics. The book is structured into several chapters, each focusing on a specific aspect of fractal geometry. It also includes an appendix with definitions, notation, examples, and references. The second edition, published in 2007, includes updates and changes based on feedback from readers and recent research, such as increased emphasis on packing measure and new examples like the Barnsley leaf and Julia set.