From Geometry to Topology (Dover Books on Mathematics) by H. Graham Flegg (PDF)

Description

This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.

User’s Reviews

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

⭐This book would be very useful guide to see what “Topology” is, before jumping into the ocean of proof.While most OTHER topology books have the format of “Definition-Theorem-Proof-…(repeat)…-Exercise” with very few motivation, THIS book contains tons of figures and clear explanation on the assumption, logical flow, interpretation, and applications.Especially, it gives 10-page long summary of topology at the last chapter: It covers all important concepts (closure, open cover, complete, connected, compact) with down-to-earth examples.It is very useful to have a taste of topology without long list of prerequisites in pure math.

⭐I gather this was written quite a while back, but I think it is quite fundamental stuff, so that shouldn’t matter. My university math courses didn’t get into topology to any extent, so I came to it as a relative newcomer. It seemed like a nice introduction to the topic, fairly light on proofs and rigor but covering the concepts in a nice intuitive manner.

⭐This book is neither a textbook nor a rigorous buildup of topology from geometry. It’s a simple and conceptual bridge from congruence classes in geometry, and basic ideas from map theory, into topology. For anyone wanting to get a grasp of the subject, I would recommend this book as a primer to any more conventional treatment of topology. In many texts, you are given general theorems in terms of sets, with little intuitive motivation. From Geometry to Topology provides the necessary background. And it’s fun to read.

⭐As the author states, this is not a text, it’s background information for those wanting to know what topologists find interesting, since the intro courses focusing on abstract principles can never get to the interesting stuff (i.e. what is interesting to most people). This book does not provide the logical foundations for a thorough understanding of topology, but it DOES provide ample fodder for thought and for seeing what issues are ultimately addressed by a study of the subject.

⭐It is an amazing book that every beginner who is interested in Topology should read!Actually, it is the one of the two books that he must read, before starting a “university” book with the tremendous amount of definitons, theorems and formulae. The other book is Dr. Arnold’s Intuitive Concepts in Elementary Topology.

⭐When I recently began studying introductory, but also quite rigorous texts on topology, on a self-taught basis, I occasionally had the thought, might this be a solution in search of a problem? As it happens, there most certainly is a most practical motivation from geometry to topology, one could say a bridge from the one to the other (no relation to Koenigsberg), and H. Graham Flegg marvelously explains just exactly what this bridge is all about.

⭐I bought this book shortly after my introductory analysis professor had once mentioned what is topology. That was the first topology book I had read, and I fell in love with the subject ever since. It’s easy to understand,and very enlightening as well.The book walks you through the transition from geometry to topology, then eleborates on several basic topological concepts.Very interesting stuff !

⭐This book is quite pictorial and thus easy to read, as it’s intended to be: a first introduction on undergraduate level to topology. However, it’s a pity it doesn’t go into topology very much. It stays very informal.

⭐I discovered Graham Flegg’s book in 1999, when working as a Statistician, having a wider interest in Mathematics generally. A few years later, I had the good fortune to study the Open University’s Topology course M435, in which (in the TV programmes accompanying the course) Flegg delivered more of the teaching which has given the teachers of the O.U. a justly deserved reputation for being first-rate communicators. Apart from clear exposition, the diagrams are very good, and the problems at the end seem to be set at just the right level. The book is not a comprehensive textbook, but a means of encouraging and stimulating an interest in the subject. This is just the kind of thing that is needed to help people with a budding interest in a subject bridge the gap to more advanced studies – and it is a very nice book to come back to, after a first course, for those who will not go further.I strongly recommend this book to anyone curious about the subject of its title. It should be a very good preparation for anyone contemplating taking an undergraduate course in Topology. Dover are to be commended for bringing it out in a cheap paperback edition.

⭐When I recently began studying introductory, but also quite rigorous texts on topology, on a self-taught basis, I occasionally had the thought, might this be a solution in search of a problem? As it happens, there most certainly is a most practical motivation from geometry to topology, one could say a bridge from the one to the other (no relation to Koenigsberg), and H. Graham Flegg marvelously explains just exactly what this bridge is all about.

⭐Not the best of books to introduce the ideas of topology. It should be clearer with more practicalexamples.

⭐An excellent introduction to topology, a very abstract subject but whose applications to physics, to exact and social sciences have grown exponentially in the latter years. The only prerequisite are high school algebra and geometry, and should be read by all first-year students of a scientific subject (mathematics, physics, chemistry, biology,..).This books is essential to begin study topology, an excellent complement is the classic volume by Paul Alexandroff, “Elementary concepts of topology”, or that of B.H. Arnold, “Intuitive Concepts in Elementary Topology “, in the same series.To continue in a more advanced study and to see the details of recent applications one can see Adams-Franzosa, “Introduction to Topology Pure and Applied”.

⭐For someone with two degrees in Mathematics … received at both side of Atlantic Ocean … it is interesting how this book has been written … how elegant is … and inspirational may be for High School and Universities.Good!

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