A General Topology Workbook

1. Front Matter

   Pages i-viii

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2. Exercises

   1. Front Matter

      Pages 1-1

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   2. Topological Spaces

      • Iain T. Adamson

      Pages 3-18

   3. Mappings of Topological Spaces

      • Iain T. Adamson

      Pages 19-22

   4. Induced and Coinduced Topologies

      • Iain T. Adamson

      Pages 23-30

   5. Convergence

      • Iain T. Adamson

      Pages 31-41

   6. Separation Axioms

      • Iain T. Adamson

      Pages 43-55

   7. Compactness

      • Iain T. Adamson

      Pages 57-64

   8. Connectedness

      • Iain T. Adamson

      Pages 65-70

3. Answers

   1. Front Matter

      Pages 71-71

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   2. Answers for Chapter 1

      • Iain T. Adamson

      Pages 73-90

   3. Answers for Chapter 2

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      Pages 91-94

   4. Answers for Chapter 3

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      Pages 95-102

   5. Answers for Chapter 4

      • Iain T. Adamson

      Pages 103-112

   6. Answers for Chapter 5

      • Iain T. Adamson

      Pages 113-129

   7. Answers for Chapter 6

      • Iain T. Adamson

      Pages 131-140

   8. Answers for Chapter 7

      • Iain T. Adamson

      Pages 141-148

4. Back Matter

   Pages 149-152

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This book has been called a Workbook to make it clear from the start that it is not a conventional textbook. Conventional textbooks proceed by giving in each section or chapter first the definitions of the terms to be used, the concepts they are to work with, then some theorems involving these terms (complete with proofs) and finally some examples and exercises to test the readers' understanding of the definitions and the theorems. Readers of this book will indeed find all the conventional constituents--definitions, theorems, proofs, examples and exercises­ but not in the conventional arrangement. In the first part of the book will be found a quick review of the basic definitions of general topology interspersed with a large num­ ber of exercises, some of which are also described as theorems. (The use of the word Theorem is not intended as an indication of difficulty but of importance and usefulness. ) The exercises are deliberately not "graded"-after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conven­ tional course, while others are quite difficult results. No solutions of the exercises, no proofs of the theorems are included in the first part of the book-this is a Workbook and readers are invited to try their hand at solving the problems and proving the theorems for themselves.

• Separation axiom
• Topologie
• compactness
• topology

"This well-printed, attractive little volume offers a first introduction to general topology, cast into the form of a problem collection...well-suited both for classroom use and for individual study."

—Publ. Math. Debrecen

"Ideal for independent study."

—The American Mathematical Monthly

• Department of Mathematics and Computer Science, Dundee, Scotland

  Iain T. Adamson

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