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Elements of Point Set Topology.

Baum, John

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ISBN 10: 0486668266 / ISBN 13: 9780486668260
Verlag: Dover, New York, 1991
Gebraucht Zustand: Very Good Softcover
Verkäufer Plurabelle Books Ltd (Cambridge, Vereinigtes Königreich)

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150p paperback with green patterned cover, spine, edges and cover yellowed but pages clean and unmarked, very good. Buchnummer des Verkäufers PAB 66522

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Bibliografische Details

Titel: Elements of Point Set Topology.

Verlag: Dover, New York

Erscheinungsdatum: 1991

Einband: Soft cover

Zustand:Very Good

Über diesen Titel

Inhaltsangabe:

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.

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