Re: Download General Topology Willard Pdf Pdf
Tommye Hope
Though there are several posts discussing the reference books for topology, for example best book for topology.But as far as I looked up to, all of them are for the purpose of learning topology or rather on introductory level.
I am wondering if there is a book or a set of books on topology like Rudin's analysis books, S.Lang's algebra, Halmos' measure (or to be more updated, Bogachev's measure theory), etc, serving as standard references.
In the end, I only have the interest on general-topology (topological space, metrization, compactification...), and optionally differential topology (manifolds). So please don't divert into algebraic context.
For general topology, it is hard to beat Ryszard Engelking's "General Topology". It starts at the very basics, but goes through quite advanced topics. It may be perhaps a bit dated, but it is still the standard reference in general topology.
The following 3 volume set (translated from Russian, edited by A. V. Arhangelskii) deserves to be mentioned among references for general topology, too.It is part of Encyclopaedia of Mathematical Sciences series.
The first part is a geometric account of general topology, with motivation for definitions and theorems, starting with the neighbourhood axioms, as more intuitive, and then proceeding to open sets, etc. There is a gradual introduction to universal properties, so that topologies are often defined in order to be able to construct various kinds of continuous functions. It has a lot on identification spaces, adjunction spaces, finite cell complexes, and also an introduction to a topology on function spaces to give a convenient category of spaces.
One other old stand-by is J.L. Kelley's General Topology, published as GTM 27. It is quite good especially if you are approaching the topic with the eye of an analyst. (In the preface he professed that he wanted to subtitle the book "What Every Young Analyst Should Know".)
Kazimier Kuratowski has written a two volume treatise on Topology which focuses more on General Topology. There is also an English translation available. I did not read it entirely, but by reading a few excerpts and looking through the contents it seems to be quite comprehensive.
Another book which might be worth mentioning in this context (although this is different from other books mentioned here; it contains overview of many various areas, but no proofs of the results given there):
Because the book is designed for the reader who wants to get a general view of the terminology with minimal time and effort there are very few proofs given; on occasion a sketch of an argument will be given, more to illustrate a notion than to justify a claim.
A reader who wants to study the subject matter of one or more of the articles systematically (or who wants to see the proof of a particular result) will find sufficient references at the end of each article as well as in the books in our list of standard references.
Topology without tears of Sidney Morris is a great book to learn topology. It's written in a very attractive way, has a lot exercises and covers a great deal of material in general topology and some material in real analysis. It has been updated recently and now has 12 chapters instead of 10 when is was firstly released. It has also appendices that include Hausdorff dimension, dynamical systems, set theory filters and nets and other topics. I read that it will be updated in the future and will contain 15 chapters and more appendices. You can download for free everywhere but I insist to try finding the recent updated version that I mentioned above. My personal opinion is that this book is like a bible for someone who likes general topology.
A fairly streamlined book, although initially gentle, is Essential Topology by Crossley. It goes up to homotopy and homology. See also Celebrating Swansea University Authors to view Crossley talking about his book.
I'd recommend a combination. Topology by Munkres for the point set stuff, and Algebraic Topology by Hatcher for the algebraic topology. You get all the advantages of two more specialized textbooks, and since Hatcher's text is free, your students won't need to buy two textbooks.
It takes a geometric approach, and at the same time a categorical view, that is, there is an emphasis on constructing continuous functions. The approach to the fundamental group via groupoids goes a long way beyond a first course, but then the results go beyond other books, for example on the fundamental group(oid) of an orbit spaces, and a gluing theorem on homotopy equivalences.
I'm fond of Wilson Sutherland's book Introduction to Metric and Topological Spaces. It covers topics such as completeness and compactness extremely well. In particular, the motivation of compactness is the best I've seen. (It doesn't do any algebraic topology, though.) I just taught a class using it, and it was generally well liked.
Introduction to Topology: Pure and Applied, by Colin Adams and Robert Franzosa.Immediately after proving that there is no retraction from the disk onto its circle boundary, they use degree theory to analyze sudden cardiac death.There is a chapter on knots, a chapter on dynamical systems, sections on Nash equilibriumand digital topology, a chapter on cosmology.
Chapter 1-4 are one of the best approaches to the topology I have ever seen. The students learn the concepts fast, their theoretical language to explicate honed, and their visualization skills improved. From chapter 5 and on it provides one of the most modern theoretical works in Topology and group theory and their inter-relationships. The exercises are superbly chosen and the examples are wonderful in pushing the theory forwards. Both the language and presentation are modern and allows for much room for visualization computational development.
The notes from when I learned topology were eventually published as a UTX book called "A taste of topology" by Volker Runde. It starts with metric spaces but ends at the same place your intended course.
Willard's General Topology is my favourite book on point-set topology (together with Bourbaki, but the latter is not suited as course text for several reasons). It also defines the fundamental group, but doesn't really do anything with it.
I'm assuming that the students are not familiar with point-set topology and it's the first course in topology for them. I'd recommend a combination of Munkres and Intuitive topology by V. V. Prasolov. There will be a great deal of precision and intuition all together.
A book that I find very readable is "Topology" by John G. Hocking and Gail S. Young. I have little teaching experience, but I remember being a student and based on that I believe that a few years ago I would have also liked this book.
I am an undergraduate student. I think that when you begin to study a new subject it is better to start from books not too broad. For a basic course in topology, I recommend these books (based on my experience as student)
While all the texts mentioned so far have sort of been aimed at developing the skill set necessary to learn algebraic/differential topology, there is a book Introduction to Topology and Modern Analysis by Simmons that is instead aimed at the topology most immediately relevant to analysis. It comes very highly recommended for those interested in that niche.
Finally, John Stillwell wrote a book Classical Topology and Combinatorial Group Theory which has a very interesting presentation and selection of material is atypical. But it seems like a pretty interesting angle of approach.
In terms of general topology, unusual features are the motivation for the open set axioms for a topology; a categorical approach, using universal properties in a clear way, thus giving an emphasis on constructing continuous functions; a geometric approach, using adjunction spaces; a gluing theorem for homotopy equivalences; and much else.
This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields. The material here is sufficient for a variety of one- or two-semester courses, and presupposes a student who has successfully mastered the material of a rigorous course in advanced calculus or real analysis. Thus it is addressed primarily to the beginning graduate student and the good undergraduate.
A principal goal here has been to seek some sort of balance, in the treatment, between two broad areas into which general topology might (rather arbitrarily and, of course, inaccurately) be divided. The first, which could be called continuous topology, centers on the results about compactness and metrization which are the indispensable tools of the modern analyst. This is what Kelley has labeled what every young analyst should know, and is represented here by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces and function spaces. The second area, which might be called geometric topology, is primarily concerned with the connectivity properties of topological spaces and provides the cores of results from general topology which are necessary preparation for later courses in geometry and algebraic topology. This core is formed here by a series of nine sections on connectivity properties, topological characterization theorems and homotopy theory. By suitable surgical intervention, mixed audiences can be taught a mixture of the two approaches, using whatever recipe the instructor likes best. To aid in the concoction of such recipes this preface is followed by a table of some of the important topics in the book together with a list of the material which is prerequisite for each.
While trying to maintain the balance just described, I have also tried to keep in mind the potential uses of such a book both as a text and as a reference source. Thus, in a concession to pedagogy, I have paced the book rather more slowly at the beginning than at the end and have concentrated motivational comments at the beginning. I have also attempted to keep the pedagogical lines of force transparent by paring the material of each section down to what I believe is fundamental. At the same time, I have included a large selection of exercises (over 340, each containing several parts), which provide drill in the techniques developed in the text, develop limiting counterexamples and provide extensions of, and parallels to, the theory presented in the text. Some of the theoretical exercises are suitable for extended development and discussion in the classroom, and all should enhance the value of the book as a reference source. Worth particular mention are the exercises on normed linear spaces and topological groups, and many of the exercises in the sections on compactness, compactification, metrization and the Stone-Weierstrass theorem. To facilitate its use as a reference source, I have included at the end of the book a collection of background notes for each section, a large (but certainly not exhaustive) bibliography and an index as comprehensive as my patience would allow.
b1e95dc632