elementary concepts of topology dover books on mathematics

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Elementary Concepts Of Topology

Author : Paul Alexandroff
ISBN : 9780486155067
Genre : Mathematics
File Size : 31. 39 MB
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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Intuitive Concepts In Elementary Topology

Author : B.H. Arnold
ISBN : 9780486275765
Genre : Mathematics
File Size : 78. 54 MB
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Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

Basic Concepts Of Algebraic Topology

Author : F.H. Croom
ISBN : 9781468494754
Genre : Mathematics
File Size : 60. 66 MB
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This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Introduction To Topology

Author : Bert Mendelson
ISBN : 9780486135090
Genre : Mathematics
File Size : 68. 94 MB
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Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

An Introduction To Algebraic Topology

Author : Andrew H. Wallace
ISBN : 9780486152950
Genre : Mathematics
File Size : 52. 66 MB
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This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

A Combinatorial Introduction To Topology

Author : Michael Henle
ISBN : 0486679667
Genre : Mathematics
File Size : 31. 19 MB
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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Elementary Topology

Author : Michael C. Gemignani
ISBN : 0486665224
Genre : Mathematics
File Size : 72. 20 MB
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Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.

First Concepts Of Topology

Author : William G. Chinn
ISBN : 0883856182
Genre : Mathematics
File Size : 23. 75 MB
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Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.

Elements Of Point Set Topology

Author : John D. Baum
ISBN : 9780486668260
Genre : Mathematics
File Size : 31. 78 MB
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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.

Topology

Author : Donald W. Kahn
ISBN : 0486686094
Genre : Mathematics
File Size : 81. 64 MB
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Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.

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