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Convergence Foundations of Topology
Paperback
ISBN13: 9789814571524
Publisher: World Scientific Publishing Company
Published: Jun 30 2016
Pages: 568
Weight: 1.85
Height: 1.20 Width: 6.10 Depth: 8.90
Language: English
It is clear that the book, with its high level of scholarship, is a labour of love on the part of its authors, and it will no doubt make quite a dent in the right circles ... The mature reader, disposed to this way of redoing topology, will have a great time.
Mathematical Association of America
This textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets.
Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis.
Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.
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