Topology: Point-Set and Geometric 1st Edition by Paul L. Shick (PDF)

Description

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which “capstone” best suits his or her students.Topology: Point-Set and Geometric features:A short introduction in each chapter designed to motivate the ideas and place them into an appropriate contextSections with exercise sets ranging in difficulty from easy to fairly challengingExercises that are very creative in their approaches and work well in a classroom settingA supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs

User’s Reviews

Editorial Reviews: Review “Ideally suited for an introductory course in topology at the junior/senior level.” (CHOICE, September 2007) From the Inside Flap The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which “capstone” best suits his or her students.Topology: Point-Set and Geometric features:A short introduction in each chapter designed to motivate the ideas and place them into an appropriate contextSections with exercise sets ranging in difficulty from easy to fairly challengingExercises that are very creative in their approaches and work well in a classroom settingA supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs From the Back Cover The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors.Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which “capstone” best suits his or her students.Topology: Point-Set and Geometric features:A short introduction in each chapter designed to motivate the ideas and place them into an appropriate contextSections with exercise sets ranging in difficulty from easy to fairly challengingExercises that are very creative in their approaches and work well in a classroom settingA supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs About the Author PAUL L. SHICK, PhD, is Professor in the Department of Mathematics and Computer Science at John Carroll University in Cleveland, Ohio. He earned a PhD in Mathematics from Northwestern University in 1984, working in the area of stable homotopy theory. He remains active in research in algebraic topology. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I believe this book to be better organized than Munkres, although Munkres is still a great book. I agree with Professor Shick that an introductory topology course should start with the definition of a topology and not that of a metric space. It allows for more general or abstract thought processes. This book is also great for self-study, although you may have to go a professor to check your solutions to the exercises as there’s none at the back of the book. So far I’m on chapter 5 and the one critique I have is that I wish there was a bit more commentary for product spaces. Do the exercises.

⭐I don’t know what the other reviewer was smoking but it certainly must have been potent stuff.In an effort to allow a broader audience to learn Topology Mr. Shick dumbs down the material to a level where it’s almost useless. Almost all of the proofs follow from definitions, others from logical manipulation of already proved theorems e.g. contraposition (which doesn’t belong in a class at this level), and very very few require actual construction. The most difficult problems, relative to the gag problems, have hints that all but give the solution. But most likely these won’t even be assigned work!What’s most telling is that these most difficult problems are actually stolen (borrowed?) straight from Munkres’ “A first course in Topology.” Now that’s fine when doing problems as homework because Shick is in effect weening us dummies onto these more difficult problems with hints. What’s not acceptable is that Professors will then use problems from Munkres’ book on exams with disregard for the fact that Shick’s book only prepares you to solve such problems with the assistance of hints. And I don’t mean psychologically either. There were several places where Munkres’ development of the material included things that are not included in Shick’s and yet the same problems were assigned at the end of the section.Anyway even if you’re studying this on your own, though the previous statements still are relevant, the book has other pedagogical flaws. The discrete and indiscrete topologies are used as examples for absolutely everything! In my opinion that provides nothing, other than a feeling of “geewiz”. The same types of things are proven over and over again instead of being relegated to problems. “If (X,t) is _____ and A is a subspace of (X,t) then A is ____.” Such and such is a topological property must’ve been proven in every chapter for at least twice.And it’s a first printing so there’s publishing mistakes everywhere. The worst of which is that the index is 2 pages behind, meaning that if it says something is on page 68 then it’s actually on 66.Study from Munkres’ book, the first chapter alone is worth more than this entire book. I hate to be mean but there’s a reason why Mr. Shick teaches at John Carroll University and Munkres teaches at MIT. I greatly regret that my professor picked this book for our class. I give it two stars out of charity and pity for Mr. Shick’s soul.

⭐Overall, this book was a wonderful introduction to the field of Topology. At times the author is a little cryptic, although it is hard not to be given the subject matter. Proofs are well-organized and documented and there is no shortage of them. This book offers a great introduction to Topology for any undergraduate with at least a background in Abstract Algebra and Set Theory.

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