Book Description

This is an introductory text which presents fundamental concepts from the subject areas of Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive prelimi- nary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, product and quotient spaces, embedding and metrization and compact, uniform and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. Each chapters includes many illustrative worked examples. At the end of each chapter there is a collection of exercises which range in difficulty. Many new ideas are presented in the exercises and so the students should be encouraged to read all the exercises. The book concludes with an extensive index that provides supplementary material on elementary topolog. The purpose of preparing these notes is to condense into an introductory text the basic definitions and techniques arising in General Topology. In particular, the material is presented to develop a basic understanding of the mathematical concepts associated with topological concepts which arise in many areas of mathematical applications. From these basic concepts one can go onto develop more sophisticated models of applied mathematics. The material is presented in an informal manner and uses mathematics which minimizes excessive formalism.