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Topology For Analysis

Author: Albert Wilansky
Publisher: Courier Corporation
ISBN: 0486469034
Size: 35.38 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.

Counterexamples In Topology

Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 0486319296
Size: 62.39 MB
Format: PDF
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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.

Modern Methods In Topological Vector Spaces

Author: Albert Wilansky
Publisher: Courier Corporation
ISBN: 0486493539
Size: 70.38 MB
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"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--

Undergraduate Topology

Author: Robert H. Kasriel
Publisher:
ISBN: 9780486474199
Size: 73.18 MB
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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.

Introductory Real Analysis

Author: A. N. Kolmogorov
Publisher: Courier Corporation
ISBN: 0486134741
Size: 37.42 MB
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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.

Introduction To Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Size: 21.88 MB
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Topology

Author: John G. Hocking
Publisher: Courier Corporation
ISBN: 0486141098
Size: 57.61 MB
Format: PDF, ePub
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Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.

Elements Of Point Set Topology

Author: John D. Baum
Publisher: Courier Corporation
ISBN: 0486668266
Size: 47.53 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.

Real Variables With Basic Metric Space Topology

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486151492
Size: 53.10 MB
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.

Topology

Author: George McCarty
Publisher: Courier Corporation
ISBN: 0486450821
Size: 14.93 MB
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This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.