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Synopsis
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
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11 of 11 people found the following review helpful
Format:Paperback
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 the last year it was presented, 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.
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.
4 of 4 people found the following review helpful
Format:Paperback
First let me declare a prejudice: Introductory texts that present topology in an axiomatic manner divorced from geometry are IMO fit only for burning. Topology grew out of geometry and IMO cannot be properly understood without at least tracing the evolution of ideas from congruence to homeomorphism. In this book Flegg does just that. The text is mostly clearly written and the presentation mostly logically sequenced and well paced. Above all the text is aptly and generously illustrated with line and half-tone graphics.
I have, however, two minor gripes about it. First, the chapters on maps and networks set the scene for combinatorial topology but the book addresses that part of topology far more briefly than it does point-set topology. This and the sub 200 page-count made it for me a slightly disjointed read. Second, in talking about the connectedness of manifolds, the description of cut operations is in places - and *despite* the diagrams - insuccinct to the point where it can cause confusion. This, IMO, is a more unfortunate feature than the disjointedness.
In the foreword, Flegg describes the text as, "... not meant to be a substitute for a serious formalised study of topological ideas; it is intended to do little more than give a list of the dramatis personae, to indicate where the 'plot' might possibly lead, and to raise the curtain on the scene for the first act". IMO it does it well - at least to the point where one who has read it could then move onto Hilbert and Cohn-Vossen without too much difficulty - and for that alone its relatively minor shortcomings are eminently forgivable.
I have, however, two minor gripes about it. First, the chapters on maps and networks set the scene for combinatorial topology but the book addresses that part of topology far more briefly than it does point-set topology. This and the sub 200 page-count made it for me a slightly disjointed read. Second, in talking about the connectedness of manifolds, the description of cut operations is in places - and *despite* the diagrams - insuccinct to the point where it can cause confusion. This, IMO, is a more unfortunate feature than the disjointedness.
In the foreword, Flegg describes the text as, "... not meant to be a substitute for a serious formalised study of topological ideas; it is intended to do little more than give a list of the dramatis personae, to indicate where the 'plot' might possibly lead, and to raise the curtain on the scene for the first act". IMO it does it well - at least to the point where one who has read it could then move onto Hilbert and Cohn-Vossen without too much difficulty - and for that alone its relatively minor shortcomings are eminently forgivable.
3 of 3 people found the following review helpful
Format:Paperback
This book should be recommended, in my opinion, to all younger mathematicians willing to study topology, because of building a bridge and filling a gap between known schemes of geometry to further and deeper topological concepts. Many young students are involved in formalized and abstract presentation of topology, without any idea of very valuable and historical geometrical background. In this approach, emphasizing old concepts and classical beauty of Euclidean geometry, topological properties are made quite obvious, necessary and easily understandable in a unique, hard to forget manner. I am sorry for not possessingFrom Geometry to Topology valuable book in my beginner's days.
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