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Principles of Topology

Principles of Topology Author Fred H. Croom
ISBN-10 9780486801544
Release 2016-02-17
Pages 336
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Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.



Undergraduate Topology

Undergraduate Topology Author Robert H. Kasriel
ISBN-10 0486474194
Release 2009-01-01
Pages 285
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General topology offers a valuable tool to students of mathematics, particularly in courses involving complex, real, and functional analysis. This introductory treatment is essentially self-contained, and it features explanations and proofs that relate to every practical aspect of point-set topology. It will prove valuable to undergraduate mathematics majors as well as to graduate students and professionals pursuing mathematics research. Author Robert H. Kasriel, who taught at Georgia Tech for many years, begins with reviews of elementary set theory and Euclidean n-space. The following chapters offer detailed studies of metric spaces and applications to analysis. A survey of general topological spaces and mappings includes considerations of compactness, connectedness, quotient spaces, net and filter convergence, and product spaces. Nearly every one of the 112 sections in this book concludes with a set of exercises that reinforce materials already covered and prepare students for subsequent chapters.



Topology

Topology Author Donald W. Kahn
ISBN-10 0486686094
Release 1975
Pages 217
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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.



Basic Concepts of Algebraic Topology

Basic Concepts of Algebraic Topology Author F.H. Croom
ISBN-10 9781468494754
Release 2012-12-06
Pages 180
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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.



Experiments in Topology

Experiments in Topology Author Stephen Barr
ISBN-10 9780486152745
Release 2012-12-04
Pages 210
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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.



Counterexamples in Topology

Counterexamples in Topology Author Lynn Arthur Steen
ISBN-10 048668735X
Release 1995
Pages 244
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Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.



Topology for Analysis

Topology for Analysis Author Albert Wilansky
ISBN-10 9780486469034
Release 2008-10-17
Pages 383
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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

A Combinatorial Introduction to Topology Author Michael Henle
ISBN-10 0486679667
Release 1979
Pages 310
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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.



A Geometric Introduction to Topology

A Geometric Introduction to Topology Author Charles Terence Clegg Wall
ISBN-10 0486678504
Release 1993
Pages 168
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First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.



General Topology

General Topology Author John L. Kelley
ISBN-10 9780486820668
Release 2017-03-07
Pages 320
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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.



A First Course in Topology

A First Course in Topology Author Robert A Conover
ISBN-10 9780486780016
Release 2014-05-21
Pages 272
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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 Topology

Introduction to Topology Author Bert Mendelson
ISBN-10 9780486135090
Release 2012-04-26
Pages 224
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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.



Topology

Topology Author Stefan Waldmann
ISBN-10 9783319096803
Release 2014-08-05
Pages 136
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This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.



Introductory Real Analysis

Introductory Real Analysis Author A. N. Kolmogorov
ISBN-10 9780486134741
Release 2012-04-25
Pages 416
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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.



General Topology

General Topology Author J. Dixmier
ISBN-10 9781475740325
Release 2013-06-29
Pages 141
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This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoing alone does not justify the very general framework in which this course is set. The fact is that the concepts mentioned above have shown themselves to be useful for objects other than the real numbers.



From Geometry to Topology

From Geometry to Topology Author H. Graham Flegg
ISBN-10 9780486138497
Release 2012-03-08
Pages 208
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Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.



Elementary Point Set Topology

Elementary Point Set Topology Author Andre L. Yandl
ISBN-10 9780486811017
Release 2016-04-10
Pages 256
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In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America