This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
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This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
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98 of 99 people found the following review helpful:
5.0 out of 5 stars
Excellent for either reference or self-teaching,
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This review is from: Topology (2nd Edition) (Hardcover)
When I was in a topology course in graduate school, I constantly returned to the Munkres book to get clearer explanations of concepts than any of the graduate-level books could provide. What is noteworthy is that the ease of understanding did NOT come at the price of shallower coverage or lack of mathematical rigor. Although this is an undergraduate text, it covers almost everything you would get in a first-year graduate course in point set topology. If you want to learn that material for the first time without an instructor, then this is the book to use. And, if you are working in another area of mathematics, and come across words like "compact", "metric space", or "connected", and have forgotten what they mean, go straight to Munkres. He always talks to you like a real human being.
64 of 65 people found the following review helpful:
5.0 out of 5 stars
Flawless introductory topology text,
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This review is from: Topology (2nd Edition) (Hardcover)
This is a fantastic book, the type of perfection to which all writers of mathematical texts should aspire. There are plenty of definitions, theorems, and proofs, as well as informative examples and prose exposition. The expository text is what makes this book really stand out. Munkres explains the concepts expressed abstractly in theorems and definitions. That is, he builds motivations for the necessarily abstract concepts in topology. This greatly improves the readability of the book, making it accessibly to general readers in mathematics, science, and engineering.The book is divided into two sections, the first covering general, i.e. point-set, topology and the second covering algebraic topology. Exercises (without solutions) are provided throughout. The exercises include straight-forward applications of theorems and definitions, proofs, counter-examples, and more challenging problems. My only complaint with this book is that it does not discuss manifolds and differentiable topology, but other texts fill this gap. I highly recommend this book to anyone interested in studying topology; it is especially well-suited for self study.
68 of 72 people found the following review helpful:
5.0 out of 5 stars
One of the best rigorous introductions to topology!,
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This review is from: Topology (2nd Edition) (Hardcover)
I used to own the 1975 (first) edition of this title since the late 1990s, but quite recently purchased the new edition as well, and donated the old book to our campus library. Despite having very close similarity to the text by Stephen Willard (1970, Dover issue 2004) which points to the fact that both authors must have used the same source articles, Munkres's book stands out as one of the best rigorous introductions for a beginning graduate student. It covers all the standard material for a first course in general topology starting with a full chapter on set theory, and now in the second edition includes a rather extensive treatment of the elementary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they were needed, many diagrams provided, the chapter exercises relevant with the correct degree of difficulty, and there are virtually no typos. The 2nd edition fine-tunes the exposition throughout, including a better paragraph formatting of the material and also greatly expands on the treatment of algebraic topology, making up for 14 total chapters as opposed to eight in the first edition.
I particularly found useful the discussion of the separation axioms and metrization theorems in the first part, and the classification of surfaces and covering spaces in the second part. In my opinion, after going through the discussion of algebraic topology in Munkres, the students should be ready to move forward to a (now standard) text such as Hatcher, for further coverage of homotopy, homology and cohomology theories of spaces. Eventhough a few contending general topology texts --such as a recent title published in the Walter Rudin Series-- have started to hit the academic markets, Munkres will no doubt remain as the classic, tried-and-trusted source of learning and reference for generations of mathematics students. This is despite the fairly high price tag which could stop some students from buying their own copies, hence encouraging instructors to choose some of the much cheaper topology paperbacks readily available through the Dover publications. Also the majority of the Munkres readers would have wished to see more hints and answers provided at the back so as to make the text more helpful for self-study. Those merely testing the waters in topology should try Fred H. Croom's 1989 text, since the latter is a more accessible title similar in the exposition and selection of topics on Munkres (and Willard for that matter), thus nicely serving as a prerequisite for either of the more advanced books. A couple of ending remarks: A reviewer has correctly mentioned here that Dr. Munkres does not include differential topology in his presentation. This is because of the length consideration, given that he has already written a separate monograph on the topic. In fact it's also necessary to first get a handle on a fair amount of algebraic topology such as the notions of homotopy, fundamental groups, and covering spaces for a full-fledged treatment of the differential aspect. In any case, one high-level reference for a rigorous excursion into this area is the Springer-Verlag GTM title by Morris W. Hirsch which includes introductions to the Morse and cobordism theories. I'd also like to mention that another decent book on general topology, unfortunately out of print for quite some time, is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would complement Munkres, as for instance Dugundji discusses ultrafilters and some of the more analytical directions of the subject. It's a pity that Dover in particular, has not yet published this gem in the form of one of their paperbacks.
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Inside This Book
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First Sentence:
We adopt, as most mathematicians do, the naive point of view regarding set theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
lifting correspondence, reduced edge path, standard covering map, universal extension property, box topology, finite indexed family, limit point compactness, compact convergence topology, pasting lemma, least normal subgroup, uniform limit theorem, subbasis element, neighborhood that intersects, path homotopy, tube lemma, theta space, path homotopic, constructing continuous functions, metrization theorem, positive linear map, countable intersection property, first countability axiom, finite complement topology, torus type, second countability axiom Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Seifert-van Kampen, Proof Suppose, Prove Theorem, Compare Exercise, Miss Smith, Applying Step, Constructing Compact Surfaces, Fundamental Groups of Some Surfaces, Imbedding Graphs, Imbeddings of Manifolds, Use Exercises, Use Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We adopt, as most mathematicians do, the naive point of view regarding set theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
lifting correspondence, reduced edge path, standard covering map, universal extension property, box topology, finite indexed family, limit point compactness, compact convergence topology, pasting lemma, least normal subgroup, uniform limit theorem, subbasis element, neighborhood that intersects, path homotopy, tube lemma, theta space, path homotopic, constructing continuous functions, metrization theorem, positive linear map, countable intersection property, first countability axiom, finite complement topology, torus type, second countability axiom Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Seifert-van Kampen, Proof Suppose, Prove Theorem, Compare Exercise, Miss Smith, Applying Step, Constructing Compact Surfaces, Fundamental Groups of Some Surfaces, Imbedding Graphs, Imbeddings of Manifolds, Use Exercises, Use Theorem 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 17
books:
See all 17 books this book cites
- Introduction to the Foundations of Mathematics by R.L. Wilder in Back Matter
- General Topology (Dover Books on Mathematics) by Stephen Willard in Back Matter
- Differential Topology by Victor Guillemin in Back Matter
- Counterexamples in Topology (Dover Books on Mathematics) by Lynn Arthur Steen in Back Matter
- Real and Complex Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin in Back Matter
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