PDF Ebook A First Course in Topology: Continuity and Dimension (Student Mathematical Library), by John McCleary
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A First Course in Topology: Continuity and Dimension (Student Mathematical Library), by John McCleary
PDF Ebook A First Course in Topology: Continuity and Dimension (Student Mathematical Library), by John McCleary
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How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincar� argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.
- Sales Rank: #95489 in Books
- Brand: Brand: American Mathematical Society
- Published on: 2006-04-07
- Original language: English
- Number of items: 1
- Dimensions: 8.25" h x 5.50" w x .50" l, .59 pounds
- Binding: Paperback
- 210 pages
- Used Book in Good Condition
Review
"McCleary offers a tight, purpose-built book, establishing the invariance of dimension, the rigorous structural distinction that differentiates lines from planes from higher-dimensional spaces." ---- CHOICE Magazine
"This is a beautiful little book that may well become a classic packed with fascinating material students who work through it will learn a great deal, and emerge from the process much better mathematicians than they were before they began. It deserves many such readers." ---- MAA Reviews
Most helpful customer reviews
5 of 6 people found the following review helpful.
$35 - This book is FREE online!
By Coffee
This is an awesome book, however, $35 dollars is a bit high. You can download the book online for free. If the book was $20 or less, I would say sure, but $35 for a thin soft cover......download it and review it yourself.
5 of 7 people found the following review helpful.
My First Book in Topology
By Man Kam Tam
John McCleary, the author of "A First Course in Topology: Continuity and Dimension", attempted to answer the question -- What is topology?--in his book. According to Wikipedia, topology is the study of those properties of objects that do not change when homeomorphisms are applied. John McCleary thinks that the central concept of topology is continuity, defined for the functions between the sets equipped with a notion of nearness (topological spaces). Since a coffee mug can be continuously deformed into a donut, the topological spaces of the coffee mug and donut are homeomorphic. The two spaces are the same from a topological view point.
John McCleary, the author, revealed that he spent too much time on developing the definitions when he first taught his undergraduate courses in topology. In fact, his book contains many definitions but a few examples. His strategy on presenting topology is that: "The first chapter reviews the set theory, so that the problem of topological invariance of dimension can be posed. The next five chapters treat the basic point-set notions of topology. The next two chapters treat the fundamental group of a space (equivalent spaces lead to isomorphic groups). The last two chapters focus on the combinatorial theme (simplicial complexes). We then associate the homology of the simplicial complexes, a sequence of vector spaces. This eventually leads to a proof of the topological invariance of dimension through homology."
There are hardly examples on the book. Thus the readers have hard time on applying the concepts. On the other hand, the book comes with proofs on well-known results. For example, the well-known proofs include (1) the fundamental theorem of algebra and (2) merely five Platonic solids exist.
0 of 1 people found the following review helpful.
Limited Coverage of Topology
By Indikos
The topics for an introductory text on topology are not adequately covered. The book lacks depth and topic coverage lacks breadth.
The merits of the book can evaluated online where it is available.
Instead of this book, a serious student of topology should consider Munkres, Gamelin or Kosniowski.
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