Morris S.A. Topology Without Tears

Sydney: 2017. — 645 p.This book provides a thorough grounding in general topology. There are many exercises in this book. Only by working through a good number of exercises will you master this course. I have not provided answers to the exercises, and I have no intention of doing so. It is my opinion that there are enough worked examples and proofs within the text itself, that it is not necessary to provide answers to exercises – indeed it is probably undesirable to do so. Very often I include new concepts in the exercises; the concepts which I consider most important will generally be introduced again in the text. Harder exercises are indicated by an *. Initially the book was typset using Donald Knuth’s beautiful and powerful TEX package. As the book was expanded and colour introduced, this was translated into LaTex.
This book has been, or is being, used by professors, graduate students, undergraduate students, high school students, and retirees, some of whom are studying to be, are or were, accountants, actuaries, applied and pure mathematicians, astronomers, biologists, chemists, computer graphics, computer scientists, econometricians, economists, aeronautical, database, electrical, mechanical, software, space, spatial and telecommunications engineers, finance experts, game theorists, neurophysiologists, nutritionists, options traders, philosophers, physicists, psychiatrists, psychoanalysts, psychologists, sculptors, software developers, spatial information scientists, and statisticians in Algeria, Argentina, Australia, Austria, Bangladesh, Bolivia, Belarus, Belgium, Belize, Brazil, Bulgaria, Cambodia, Cameroon, Canada, Chile, Gabon, People’s Republic of China, Colombia, Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, Ecuador, Egypt, Estonia, Ethiopia, Fiji, Finland, France, Gaza, Germany, Ghana, Greece, Greenland, Guatemala, Guyana, Honduras, Hungary, Iceland, India, Indonesia, Iran, Iraq, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea, Kuwait, Latvia, Liberia, Lithuania, Luxembourg, Malaysia, Malta, Mauritius, Mexico, New Zealand, Nicaragua, Nigeria, Norway, Pakistan, Panama, Paraguay, Peru, Poland, Portugal, Puerto Rico, Qatar, Romania, Russia, Senegal, Serbia, Sierra Leone, Singapore, Slovenia, South Africa, Spain, Sri Lanka, Sudan, Suriname, Sweden, Switzerland, Syria, Taiwan, Tanzania, Thailand, The Netherlands, Trinidad and Tobago, Tunisia, Turkey, United Kingdom, Ukraine, United Arab Emirates, United States of America, Uruguay, Uzbekistan, Venezuela, and Vietnam.The author is Sidney (Shmuel) Allen Morris, Emeritus Professor of Federation University Australia and Adjunct Professor of La Trobe University, Australia.Topological Spaces.
The Euclidean Topology.
Limit Points.
Homeomorphisms.
Continuous Mappings.
Metric Spaces.
Compactness.
Finite Products.
Countable Products.
Tychonoff’s Theorem.
Quotient Spaces.
The Stone-Weierstrass Theorem.
Infinite Sets (App. 1).
Topology Personalities (App. 2).
Chaos Theory and Dynamical Systems (App. 3).
Hausdorff Dimension (App. 4).
Topological Groups (App. 5).
Filters and Nets (App. 6).