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 : 41. 17 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 : 56. 93 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.

An Introduction To Algebraic Topology

Author : Andrew H. Wallace
ISBN : 9780486152950
Genre : Mathematics
File Size : 65. 74 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.

Basic Concepts Of Algebraic Topology

Author : F.H. Croom
ISBN : 9781468494754
Genre : Mathematics
File Size : 27. 39 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 : 45. 82 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.

Concepts Of Modern Mathematics

Author : Ian Stewart
ISBN : 9780486134956
Genre : Mathematics
File Size : 85. 46 MB
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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Topology For Analysis

Author : Albert Wilansky
ISBN : 9780486469034
Genre : Mathematics
File Size : 44. 97 MB
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Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.

A Combinatorial Introduction To Topology

Author : Michael Henle
ISBN : 0486679667
Genre : Mathematics
File Size : 28. 79 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.

First Concepts Of Topology

Author : William G. Chinn
ISBN : 0883856182
Genre : Mathematics
File Size : 70. 45 MB
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Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.

General Topology

Author : John L. Kelley
ISBN : 9780486820668
Genre : Mathematics
File Size : 44. 77 MB
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Comprehensive text for beginning graduate-level students and professionals. "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure." — Bulletin of the American Mathematical Society. 1955 edition.

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