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Author: Paul Alexandroff Publisher: Courier Corporation ISBN: 0486155064 Category : Mathematics Languages : en Pages : 68
Book Description
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.
Author: Paul Alexandroff Publisher: Courier Corporation ISBN: 0486155064 Category : Mathematics Languages : en Pages : 68
Book Description
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.
Author: Charles Terence Clegg Wall Publisher: Courier Corporation ISBN: 0486678504 Category : Mathematics Languages : en Pages : 195
Book Description
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.
Author: S.P. Novikov Publisher: Springer Science & Business Media ISBN: 3662105799 Category : Mathematics Languages : en Pages : 326
Book Description
This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.
Author: Robert A Conover Publisher: Courier Corporation ISBN: 0486780015 Category : Mathematics Languages : en Pages : 276
Book Description
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
Author: Theodore W. Gamelin Publisher: Courier Corporation ISBN: 0486320189 Category : Mathematics Languages : en Pages : 258
Book Description
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Author: John D. Baum Publisher: Courier Corporation ISBN: 0486668266 Category : Mathematics Languages : en Pages : 164
Book Description
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.
Author: Bert Mendelson Publisher: Courier Corporation ISBN: 0486135098 Category : Mathematics Languages : en Pages : 226
Book Description
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.
Author: Steven A. Gaal Publisher: Courier Corporation ISBN: 0486472221 Category : Mathematics Languages : en Pages : 338
Book Description
Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.
Author: Tai-Danae Bradley Publisher: MIT Press ISBN: 0262359626 Category : Mathematics Languages : en Pages : 167
Book Description
A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Author: Paul Alexandroff
Author: Paul Alexandroff
Author: Charles Terence Clegg Wall
Author: Fred H. Croom
Author: S.P. Novikov
Author: Robert A Conover
Author: Theodore W. Gamelin
Author: John D. Baum
Author: Bert Mendelson
Author: Steven A. Gaal
Author: Tai-Danae Bradley