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 : 77. 30 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 : 76. 46 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.

Elementary Topology

Author : Michael C. Gemignani
ISBN : 0486665224
Genre : Mathematics
File Size : 60. 79 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.

Elementary Concepts Of Topology

Author : Paul Alexandroff
ISBN : 048660747X
Genre : Mathematics
File Size : 85. 82 MB
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Alexandroff's beautiful and elegant introduction to topology was originally published in 1932 as an extension of certain aspects of Hilbert's Anschauliche Geometrie. The text has long been recognized as one of the finest presentations of the fundamental concepts, vital for mathematicians who haven't time for extensive study and for beginning investigators. The book is not a substitute for a systematic text, but an unusually useful intuitive approach to the basic concepts. Its aim is to present these concepts in a clear, elementary fashion without sacrificing their profundity or exactness and to give some indication of how they are useful in increasingly more areas of mathematics. The author proceeds from the basics of set-theoretic topology, through those topological theorems and questions which are based upon the concept of the algebraic complex, to the concept of Betti groups which binds together central topological theories in a whole and upon which applications of topology largely rest. Wholly consistent with current investigations, in which a larger and larger part of topology is governed by the concept of homology, the book deals primarily with the concepts of complex, cycle, and homology. It points the way toward a systematic and entirely geometrically oriented theory of the most general structures of space. First English translation, prepared for Dover by Alan E. Farley. Preface by David Hilbert. Author's Foreword. Index. 25 figures.

Introduction To Topology

Author : Bert Mendelson
ISBN : 9780486135090
Genre : Mathematics
File Size : 89. 56 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.

Elementare Differentialgeometrie

Author : Christian Bär
ISBN : 9783110224597
Genre : Mathematics
File Size : 52. 79 MB
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This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

Einf Hrung In Die Gruppentheorie

Author : Pawel S. Alexandroff
ISBN : 381711270X
Genre : Group theory
File Size : 46. 96 MB
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Elementary Point Set Topology

Author : Andre L. Yandl
ISBN : 9780486803494
Genre : Mathematics
File Size : 66. 63 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.

A First Course In Topology

Author : Robert A Conover
ISBN : 9780486780016
Genre : Mathematics
File Size : 78. 48 MB
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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

Introduction To Topological Groups

Author : Taqdir Husain
ISBN : 9780486828206
Genre : Mathematics
File Size : 56. 99 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.

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