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1. Introduction to Topology: Third Edition by Bert Mendelson | |
Paperback: 224
Pages
(1990-07-01)
list price: US$10.95 -- used & new: US$6.41 (price subject to change: see help) Asin: 0486663523 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (13)
Awesome book!
Overhyped
very mindful of the student
Great book for self study
An amazing read! |
2. Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach Jr. | |
Paperback: 256
Pages
(1995-09-22)
list price: US$12.95 -- used & new: US$7.77 (price subject to change: see help) Asin: 048668735X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (10)
Resource for deep knowledge of Point-Set Topology
Counterexamples in Topology
a veritable mine of information....
Essential if you want to be good in point set topology
a good book to combine with a regular textbook |
3. Topology (2nd Edition) by James Munkres | |
Hardcover: 537
Pages
(2000-01-07)
list price: US$141.33 -- used & new: US$118.72 (price subject to change: see help) Asin: 0131816292 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (32)
How good can a textbookbe?
Excellent
Incredible textbook
came in good condition
Well written, but not interesting. |
4. Introduction to Topology: Second Edition by Theodore W. Gamelin, Robert Everist Greene | |
Paperback: 256
Pages
(1999-02-16)
list price: US$14.95 -- used & new: US$8.83 (price subject to change: see help) Asin: 0486406806 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Great book for starters
A Wonderful Book
I'm not good at math
Okay, not great. Overall, I give it a C+
excellent introduction to topology |
5. Schaum's Outline of General Topology by Seymour Lipschutz | |
Paperback: 256
Pages
(1968-06-01)
list price: US$18.95 -- used & new: US$9.99 (price subject to change: see help) Asin: 0070379882 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (9)
A Genuine Masterpiece Endowed with Eternal Beauty
Great Book
An excellent supplement for the learning of topology
Admiral Topology
General Topology |
6. Algebraic Topology by Allen Hatcher | |
Paperback: 550
Pages
(2001-11-15)
list price: US$37.99 -- used & new: US$30.01 (price subject to change: see help) Asin: 0521795400 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (19)
Terrible textbook
More Hand-Waving Than an Orchestral Conductor
Really bad as a "readable" texbookbut good reference
amazing book, but caveat emptor
excellent modern introduction |
7. Computational Topology by Herbert Edelsbrunner and John L. Harer | |
Hardcover: 241
Pages
(2009-12-08)
list price: US$59.00 -- used & new: US$50.44 (price subject to change: see help) Asin: 0821849255 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
8. Differential Topology (AMS Chelsea Publishing) by Victor Guillemin, Alan Pollack | |
Hardcover: 222
Pages
(2010-08-16)
list price: US$40.00 -- used & new: US$28.80 (price subject to change: see help) Asin: 0821851934 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (15)
great old school (60's, 70's) math book
A spectacular book
Poor beginning, good middle, ends as one long exercise.
Good book
great introduction to the subject, despite its glaring faults |
9. General Topology by Stephen Willard | |
Paperback: 384
Pages
(2004-02-27)
list price: US$22.95 -- used & new: US$11.99 (price subject to change: see help) Asin: 0486434796 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Among the best available reference introductions to general topology, this volume encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by 9 sections on connectivity properties, topological characterization theorems, and homotopy theory. Includes 340 exercises. 1970 edition. 27 figures. Customer Reviews (10)
agonizing to use as a reference
Absolutely amazing!
A Great Beginning Text
A masterpiece
Excellent |
10. Basic Topology (Undergraduate Texts in Mathematics) by M.A. Armstrong | |
Paperback: 260
Pages
(2010-11-02)
list price: US$64.95 -- used & new: US$52.25 (price subject to change: see help) Asin: 1441928197 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (11)
Useless for learning OR a reference; disorganized; unfocused.
Bad, Bad Book
A very welcome, intuitive approach to topology
Your Average topology student will be frustrated...
An acceptable text |
11. Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson | |
Hardcover: 332
Pages
(2008-09-08)
list price: US$27.95 -- used & new: US$10.95 (price subject to change: see help) Asin: 0691126771 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (12)
Topology Starter Book
This book is a real gem itself
Very Good, But Challenging
A Gem Indeed!
A gem of mathematical results produced by one of the masters of mathematics |
12. Topology from the Differentiable Viewpoint by John Willard Milnor | |
Paperback: 76
Pages
(1997-11-24)
list price: US$30.95 -- used & new: US$19.00 (price subject to change: see help) Asin: 0691048339 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (9)
it's ggrrrrrrrrrrreat!
a must-read supplement for topology students
Exactly would it should be
best math book ever written
Compact and useful |
13. Topology by John G. Hocking, Gail S. Young | |
Paperback: 384
Pages
(1988-06-01)
list price: US$16.95 -- used & new: US$10.72 (price subject to change: see help) Asin: 0486656764 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index. Customer Reviews (7)
Decent book with flaws
Very Impressed
A good start The beginning student of topology should probably read this book with the following mindset: try to think of ways and techniques that you would devise to study the structure of a topological space. Homotopy and homology (in various forms) are the standard techniques for doing this. These strategies have varying degrees of success, but their use in topology now seems to be reaching a saturation limit, even though the explicit calculation of homotopy groups is still a very active area. New techniques and concepts, representing sort of a "large deviation" from the standard ones discussed in this book, will be needed to make further progress in the study of complicated topological spaces. Something more is needed now, that is completely different than homology and homotopy theory, that will make more transparent the properties of these spaces. These new techniques will be somewhat radical from the standpoint of current ones, but they will be more effective from a conceptual (and computational) point of view.
A Professional Topologist loves this book.
Theoretical Dictionary |
14. Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley | |
Paperback: 224
Pages
(2005-07-01)
list price: US$39.95 -- used & new: US$30.74 (price subject to change: see help) Asin: 1852337826 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra. Customer Reviews (4)
Best Intro to Topology
Surely not optimal
Best undergraduate topology book
A pleasure to read |
15. Undergraduate Topology by Robert H. Kasriel | |
Paperback: 304
Pages
(2009-10-22)
list price: US$14.95 -- used & new: US$9.59 (price subject to change: see help) Asin: 0486474194 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description General topology offers a valuable tool to students of mathematics, particularly in such courses as complex, real, and functional analysis. This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 edition. Customer Reviews (2)
A Classic Work in Topology for The Undergraduate and Me, the Amateur!
a great complement to any intro analysis or topology course |
16. A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics) by J. P. May | |
Paperback: 254
Pages
(1999-09-01)
list price: US$24.00 -- used & new: US$23.94 (price subject to change: see help) Asin: 0226511839 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field. Customer Reviews (9)
If U want generalization out to infinity, this is it for you, in algebraic topology basics.
The Title Says it All
The opposite of Hatcher
Lucid and elegant, but not for beginners
A Unique and Necessary Book However, as Willard points out, mathematics is learned by successive approximation to the truth. As you becomes more mathematically sophisticated, you should relearn algebraic topology to understand it the way that working mathematicians do. Peter May's book is the only text that I know of that concisely presents the core concepts algebraic topology from a sophisticated abstract point of view. To make it even better, it is beautifully written and the pedagogy is excellent, as Peter May has been teaching and refining this course for decades. Every line has obviously been thought about carefully for correctness and clarity. As an example, ones first exposure to singular homology should be concrete approach using singular chains, but this ultimately doesn't explain why many of the artificial-looking definitions of singular homology are the natural choices. In addition, this decidedly old-fashioned approach is hard to generalize to other combinatorial constructions. Here is how the book does it: First, deduce the cellular homology of CW-complexes as an immediate consequence of the Eilenberg-Steenrod axioms. Considering how one can extend this to general topological spaces suggests that one approximate the space by a CW-complex. Realization of the total singular complex of the space as a CW-complex is a functorial CW-approximation of the space. As the total singular complex induces an equivalence of (weak) homotopy categories and homology is homotopy-invariant, it is natural to define the singular homology of the original space to be the homology of the total singular complex. Although sophisticated, this is a deeply instructive approach, because it shows that the natural combinatorial approximation to a space is its total singular complex in the category of simplicial sets, which lets you transport of combinatorial invariants such as homology of chain complexes. This approach is essential to modern homotopy theory. ... Read more |
17. From Geometry to Topology by H. Graham Flegg | |
Paperback: 208
Pages
(2001-09-04)
list price: US$14.95 -- used & new: US$9.44 (price subject to change: see help) Asin: 0486419614 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Perfect book for the right reader
Easy, but okay...
Very nice and intuitive introducation to topology |
18. Topology (Undergraduate Texts in Mathematics) by K. Jänich | |
Hardcover: 208
Pages
(1984-01-30)
list price: US$64.95 -- used & new: US$43.90 (price subject to change: see help) Asin: 0387908927 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
great as motivation but not a textbook
A simple introduction to advanced mathematical concepts
Full of motivations Since it does not have any problem sections, I can see why Munkres' book is more popular in college. It still gives some inspiring questions from time to time. Besides the basic pot-set topology, it also covers some algebraic topology and differentialtopology. The author does not hesitate to use examples from those advanced areas without formal definitions, and this was a bit annoying when I read it the first time. In this sense, the book is not really selfcontained. However, when finally a notion is formally defined, I can see it from various aspects in those examples. This really helps me understand topology better, and makes me want to explore them. After reading the existence thm of covering spaces in chapter 9, I realized that mathematics is really an art. The index in the back of the book is in the format of short definitions, which can be used as a quick reference.
Students: BUY THIS BOOK!!! At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: "If is often said against intuitive, spatial argumentation that it is not really argumentation but just so much gesticulation - just 'handwaving'. Shall we then abandon all intuitive arguments? Certainly not. As long as it is backed by the gold standard of rigorous proofs, the paper money of gestures is an invaluable aid for quick communication and fast circulation of ideas. Long live handwaving!". This has to rank as one of the best paragraphs that has every appeared in a mathematics book, for it nicely summarizes the need for developing a feel for the concepts behind mathematics before moving on to the rigorous proofs. Physicists in particular, who must assimilate mathematics very quickly in order to apply it to real problems must have a pictorial, "playful" understanding of the mathematical constructions. Thus the language that the author employs is informal, and a listing of the best discussions in the book would really entail a listing of every one in the book. There is not one part of the book that is not helpful or interesting, and the author delves into many different areas that involve the use of topology. If you are a beginning student in mathematics, BUY AND STUDY THIS BOOK...BUY AND STUDY THIS BOOK. You will take away so much for the price paid.
Excellent |
19. First Concepts of Topology (New Mathematical Library) by William G. Chinn | |
Paperback: 160
Pages
(1975-06)
list price: US$21.95 -- used & new: US$21.95 (price subject to change: see help) Asin: 0883856182 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (2)
Good introduction to the basics of topology
Great Introduction to Topology |
20. Introduction to Topology and Modern Analysis by George F. Simmons | |
Hardcover: 384
Pages
(2003-06-01)
list price: US$64.00 -- used & new: US$63.36 (price subject to change: see help) Asin: 1575242389 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (11)
Fantastically clear
Great service!
fantastic introduction to general topology
Didactic perfection The author's attitude can only be characterized as magnificent, and, if one is to judge his utterances in the preface by what is found after it, one will indeed find perfect evidence of his delight in mathematics and his high competence in elucidating very abstract concepts in topology and real analysis. Indeed, this has to be the best book ever written for mathematics at this level. It is a book that should be read by everyone that desires deep insights into modern real and functional analysis. After a brief and informal overview of set theory, the author moves on to the theory of metric spaces in chapter 2. His emphasis is on the idea that metric spaces are easy to find, since every non-empty set has the discrete metric, and that metric spaces are good motivation for the more general idea of a topological space. The Cantor set, ubiquitous in measure theory, dynamical systems, and fractal geometry, is constructed as the most general closed set on the real line, i.e. one obtained by removing from the real line a countable disjoint class of open intervals. Continuity of mappings between metric spaces is defined, and also the concept of uniform continuity, the latter of which is motivated very nicely by the author. Then, the author takes the reader to a higher level of abstraction, wherein he asks the reader to consider all of the continuous functions on a metric space, and turn this collection into a metric space of a special type called a normed linear space, and, more specifically, a Banach space. Thus the author introduces the reader to the field of functional analysis. A lengthy introduction to topological spaces follows in chapter 3. The author motivates well the idea of an open set, and shows that one could just as easily use closed sets as the fundamental concept in topology. And, most important for functional analysis, he introduces the weak topology, and shows how to obtain the weakest topology for a collection of mappings from a topological space to a collection of other topological spaces. The reader can see clearly that the weaker the topology on a space the harder it is for mappings to be continuous on the space. Compactness, so essential in all areas of mathematics that make use of topology, is discussed in chapter 4. It is motivated by an abstraction of the Heine-Borel theorem from elementary real analysis, and the author shows how well-behaved things are on compact topological spaces. Some important theorems are proved in this chapter, namely Tychonoff's theorem, the Lebesgue covering lemma, and Ascoli's theorem. Recognizing that the only functions able to be continuous on a space with the indiscrete topology are the constants, and that a space with the discrete topology has continuous functions in abundance, the author asks the reader to consider topologies that fall between these extremes, and this motivates the separation properties of topological spaces. Chapter 5 is an in-depth discussion of separation, and the reader again confronts function spaces, and their ability (or non-ability) to separate the points of a topological space. Spaces that allow such separation to occur are called completely regular, and this property has far-reaching consequences in analysis and other areas of mathematics. The Stone-Cech compactification is discussed as an imbedding theorem for completely regular spaces, analogous to one for normal spaces. The intuitive idea of a space being connected is given rigorous treatment in chapter 6. Certain pathologies can of course arise when discussing connectedness, and the author shows this by discussing totally disconnected spaces, remarking that such spaces are very important in dimension theory and representation theory. Indeed, computational and fractal geometry is much harder to study because of the existence of these spaces. Chapter 7 is important to all working in numerical analysis, wherein the author discusses approximation theory. The Weierstrass approximation and the Stone-Weierstrass theorems are discussed in detail. A slight detour through algebra is given in chapter 8. Groups, rings, and fields are given a minimal treatment by the author, discussing only the basic rudiments that are needed to get through the rest of the book. Banach spaces make their appearance in chapter 9, with the three pillars of the theory proven: the Hahn-Banach, the open mapping, and the uniform boundedness theorems. These theorems guarantee that the study of Banach spaces is worth doing, and that there are analogs of the finite dimensional theory in the (infinite)-dimensional context of Banach spaces. The theory of Banach spaces is very extensive, but this chapter gives a peek at this very interesting area of mathematics. Banach spaces with an inner product are considered in chapter 10. These of course are the familiar Hilbert spaces, so important in physics and the subject of a huge amount of research in mathematics. The presence of the inner product allows constructions familiar from ordinary finite-dimensional vector spaces to carry over to the inifinite-dimensional setting, one example being the transpose of a matrix, which is replaced in the Hilbert space setting by a self-adjoint operator. As a warm-up to the infinite-dimensional theory, finite-dimensional spectral theory is considered in chapter 11. The famous spectral theorem is proven. Then in chapter 12, the reader enters the world of "soft" analysis, wherein topological and algebraic constructions are used to study linear operators on spaces of infinite dimensions. Putting an algebraic structure on a Banach space gives a Banach algebra, and then the trick is deal with the spectrum of an element of this algebra. The reader can see the interplay between algebra, topology, and analysis in this chapter and the next one on commutative Banach algebras. Indeed, the Gelfand-Naimark theorem, that essentially states that elements of a commutative Banach *-algebra act like the functions on its maximal ideal space, has to rank as one of the most interesting results in the book, and indeed in all of mathematics.
Good Classical Introduction to Banach Algebras I can attest from personal experience that the book is well-written; indeed I worked through it chapter by chapter. But today there do exist a plethora of other treatments that can at least rival this text in lucidity, organisation and coverage. For example, for general topology, there is an excellent text by Willard titled 'General Topology',as well as Hocking and Young's old 'Topology'. Both of these go much further in the realm of point-set topology than Simmons. Similarly there are any number of well-written texts on functional analysis that cover the subject of Banach spaces, Hilbert spaces and self-adjoint operators very clearly. Indeed in some respects I feel the Simmons book was inadequate by itself and needed to be supplemented by a text on linear algebra; self-adjoint operators -- and by implication, the Spectral theorem -- need to be seen and manipulated in the finite-dimensional version before one examines their infinite-dimensional generalisation. The Simmons book is a bit weak here; one needs to be playing with matrices. These are, however, minor quibbles. The book can be recommended to a junior- or senior-level undergraduate. ... Read more |
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