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 : 67. 57 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 : 51. 48 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 : 74. 36 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 : 67. 91 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.

Elementary Topology

Author : Michael C. Gemignani
ISBN : 0486665224
Genre : Mathematics
File Size : 66. 98 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.

A Combinatorial Introduction To Topology

Author : Michael Henle
ISBN : 0486679667
Genre : Mathematics
File Size : 60. 30 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.

Introduction To Topological Groups

Author : Taqdir Husain
ISBN : 9780486819198
Genre : Mathematics
File Size : 87. 96 MB
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Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

Elementary Point Set Topology

Author : Andre L. Yandl
ISBN : 9780486803494
Genre : Mathematics
File Size : 39. 49 MB
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This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition.

Experiments In Topology

Author : Stephen Barr
ISBN : 9780486152745
Genre : Mathematics
File Size : 79. 16 MB
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Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Concepts Of Modern Mathematics

Author : Ian Stewart
ISBN : 9780486134956
Genre : Mathematics
File Size : 58. 92 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.

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