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Principles of Topology
ÁöÀºÀÌ
:
Fred H. Croom
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:
Thomson
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316
ISBN
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9789812432889
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This text presents the fundamental principles of topology rigorously but not abstractly. It emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. The usual topics of point-set topology, including metric spaces, general topological spaces, continuity, topological equivalence, basis, sub-basis, connectedness , compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces are treated in this text. Most of the factual information about topology presented in this text is stated in the theorems and illustrated in the accompanying examples, figures and exercises. This book contains many exercises of varying degrees of difficulty. The notation used in this text is reasonably standard; a list of symbols with definitions appears on the front end-sheets. This text is designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels. It is accessible to junior mathematics majors who have studied multivariable calculus.
"As many math educators agree, there are many textbooks not written for beginners. This textbook is outstanding for any level of beginner. I wish it can be picked up by Dover. I highly recommend it to any reader who wants to know the subject: Topology."
"I'm an adult, self-study student, with a background in calculus, physics. I've now gone through several books on topology, and I find that even many of the undergraduate texts tend to be a bit "dense," in that they introduce too much, too fast. Croom's textbook takes a very step-by-step, hand-holding approach to introducing topology, focusing on concrete examples, yet still having a reasonable amount of rigor. (Of nine chapters, he doesn't even formally get to topology until Chapter 4. The first three chapters are a general intro, open and closed sets, and metric spaces.) The last chapter offers a basic introduction to algebraic topology. This is an excellent book for self-study, and also good for undergraduates with a physics or engineering orientation who want to get the intuitive principles, and also some sense for the formal math. Students (including undergrads) who are really strong on abstract math might benefit from the more intensive and detailed treatments found in other texts; but even they might find Croom's book useful to fall back on when they get stuck on some basic concept. Croom includes historical discussions of the foundations of topology, which is also helpful. He also includes a glossary of mathematical symbols up front, which is very helpful for trying to keep track of all the new notations involved. There are lots of solved problems, and also problems for students to work out, although solutions for those would be helpful in some future edition."
"I taught a one semester course on basic point set topology out of this book. The emphasis in the first half is on metric spaces, which provide the most natural class of examples for the basic principles of point set topology that any student taking a course in topology must know about. There is little extraneous material, and I found that the students thought the book was very good. This was a group of students at a regional campus of a large state university, and I would recommend the book for a beginning course at a comparable campus. Those teaching at research institutions will want more."
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