This work aims to present elementary topology in an unconventional way. It gives a review of the basic definitions together with exercises without solutions or proofs of the theorems in Part 1, and then presents the solutions in Part 2, allowing the student to compare answers with their own.
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"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
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1 of 3 people found the following review helpful:
4.0 out of 5 stars
A concentrated, intense way to learn general topology,
By Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews (VINE VOICE) (HALL OF FAME REVIEWER) (REAL NAME)
This review is from: A General Topology Workbook (Paperback)
This book brings back memories of a graduate course in general topology that I took as an undergraduate, which was taught via the "Moore method", after the late Robert Lee Moore, who invented it. Handouts were given to the class (there were only 3 of us), and each of us was expected to work out or prove every result in the handout, without consulting references or collaborating with other students. Theorems were to be proved, or counterexamples given, but we did not know a priori which item from the handout was actually true or false. Needless to say this took a lot of work, and all of us had to present our results on the blackboard for scrutiny by both classmates and instructor. The Moore method has its defenders and detractors. It certainly encourages originality of thought and strict intellectual honesty. Students can find incredible reinforcment as they discover that they can indeed give original proofs of sometimes very difficult (and famous) results in general topology. The downside is that not as much material is covered as compared to a traditional course in general topology. Students who are hungry to get to the frontiers of research might become impatient because of this. This book does not follow the strict methodologies that we followed in our class, but instead reveals to the reader which results are true and then encourages their proof. Readers are also lead through the construction of examples and counterexamples, allowing them to gain more of the intuition needed for a thorough understanding of general topology. It is also a good book to use for independent study, as the answers to the results are given in the book (and this actually is the major portion of its bulk).
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Inside This Book
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First Sentence:
Throughout the book we use the following standard notation: N is the set of natural numbers {0, 1, 2, . . . }; Q is the set of rational numbers; R is the set of real numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
particular point topology, finite complement topology, adherent point, separated subsets, digital topology, completely regular space, countable open cover, countably infinite subset, neighbourhood base, finite intersection property, net associated, subspace topology, topological product, dyadic rationals, countable base, topological space, disjoint open sets, finite subcover, distinguishes points, finite family, topology induced, countable dense subset Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Tihonov's Theorem, Urysohn's Lemma, Compare Exercise, Tietze's Extension Theorem, Triangle Inequality New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Throughout the book we use the following standard notation: N is the set of natural numbers {0, 1, 2, . . . }; Q is the set of rational numbers; R is the set of real numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
particular point topology, finite complement topology, adherent point, separated subsets, digital topology, completely regular space, countable open cover, countably infinite subset, neighbourhood base, finite intersection property, net associated, subspace topology, topological product, dyadic rationals, countable base, topological space, disjoint open sets, finite subcover, distinguishes points, finite family, topology induced, countable dense subset Key Phrases - Capitalized Phrases (CAPs): (learn more)
Zorn's Lemma, Tihonov's Theorem, Urysohn's Lemma, Compare Exercise, Tietze's Extension Theorem, Triangle Inequality New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 2
books:
1
book
cites this book:
- Counterexamples in Topology (Dover Books on Mathematics) by Lynn Arthur Steen on page 52
- General Topology (Dover Books on Mathematics) by Stephen Willard in Back Matter
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