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

Introduction to Topology'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.
 
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. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 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. 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. 1975 edition.
 

• Comprehensive Introduction to Topology: Offers a thorough overview of fundamental topology concepts, perfect for a one-semester course.
• Elementary Topics in Set Theory: Starts with an informal discussion of set theory, laying the groundwork for understanding mathematical structures.
• Focus on Metric Spaces: Explores metric spaces and distance functions, dedicating attention to their definition in Euclidean n-space.
• Generalization to Topological Spaces: Presents topological spaces as an extension of metric spaces, providing a broad view of topology.
• Detailed Exploration of Connectedness and Compactness: Devotes entire chapters to these core topological properties, ensuring a comprehensive understanding.
• Structured for Educational Use: Tailored for students familiar with calculus and theorem proofs, aligning with academic course structures.
• Imaginative and Instructive Exercises: Provides a range of challenging exercises that stimulate critical thinking and deepen understanding.
• Exceptional Clarity: The book is commended for its clear and concise writing style, making complex concepts accessible to undergraduate students.
• Fine Writing Style: Written with elegance, ensuring the content is engaging and easy to follow.

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.
Unabridged Dover (1990) republication of the edition published by Allyn and Bacon, Inc., Boston 1975.