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Elements Of Algebraic Topology

2018-03-05 Mathematics
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Release : 2018-03-05
Genre : Mathematics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis Elements Of Algebraic Topology by : James R. Munkres

Download or read book Elements Of Algebraic Topology written by James R. Munkres. This book was released on 2018-03-05. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

Elements of Point Set Topology

1991-01-01 Mathematics
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Release : 1991-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 266/5 ( reviews)

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Book Synopsis Elements of Point Set Topology by : John D. Baum

Download or read book Elements of Point Set Topology written by John D. Baum. This book was released on 1991-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

A Concise Course in Algebraic Topology

1999-09 Mathematics
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Release : 1999-09
Genre : Mathematics
Kind : eBook
Book Rating : 832/5 ( reviews)

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Book Synopsis A Concise Course in Algebraic Topology by : J. P. May

Download or read book A Concise Course in Algebraic Topology written by J. P. May. This book was released on 1999-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topology

2017-03-10 Topology
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Release : 2017-03-10
Genre : Topology
Kind : eBook
Book Rating : 517/5 ( reviews)

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Book Synopsis Topology by : James R. Munkres

Download or read book Topology written by James R. Munkres. This book was released on 2017-03-10. Available in PDF, EPUB and Kindle. Book excerpt: For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

Lectures on Algebraic Topology

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 568/5 ( reviews)

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Book Synopsis Lectures on Algebraic Topology by : Albrecht Dold

Download or read book Lectures on Algebraic Topology written by Albrecht Dold. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica tions of (co-)homology to homotopy. Nor does it deal with general(-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-)homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories - although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.

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