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Science & Mathematics - Introduction to Topology: Third Edition (Dover Books on Mathematics)

Description

Book Synopsis: Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book’s principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure. The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.

Details

Are you in search of a concise yet comprehensive introduction to topology? Look no further! The highly regarded Introduction to Topology: Third Edition is the perfect resource for undergraduate students. Written with exceptional clarity, this book offers a thorough survey of elementary topics in the study of mathematical structures. Whether you're a beginner or have already delved into calculus, this book is designed to help you develop a solid grasp of topology.

One of the standout features of this book is its imaginative and instructive exercises. Through hands-on practice, you'll gain a deep understanding of the fundamental concepts covered. With its fine writing style and easy-to-follow explanations, you'll find yourself engaged and motivated to learn more.

In the Introduction to Topology: Third Edition, the author begins with an informal discussion of set theory, gradually building up to more advanced topics. From metric spaces to topological spaces, each concept is introduced in a clear and logical manner. By the time you reach the chapters on connectedness and compactness, you'll have a solid foundation to tackle these important topological properties.

Dr. Mendelson, our esteemed author and former Professor of Mathematics at Smith College, has carefully structured this book to cater to your learning needs. Each chapter is designed to guide you seamlessly through the material, ensuring that you grasp the concepts at every step. Countability is covered in Chapter 5, providing a comprehensive understanding of compactness.

To enhance your learning experience, this book is filled with challenging and stimulating exercises. Put your newfound knowledge to the test and deepen your understanding of topology. Get your hands on the Introduction to Topology: Third Edition and embark on a journey of mathematical exploration like never before!

Take the first step towards mastering topology today!

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