Convergence Foundations Of Topology

Szymon Dolecki, Frederic Mynard (Autoren)

Buch | Hardcover

568 Seiten

2016
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-4571-51-7 (ISBN)

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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.

Introduction; Convergences; Pretopologies; Separation; Pseudotopologies; Compactness; Completeness; Extensions; Structural Aspects; Spaces of Maps; Connectedness; Metrizability and Complete Metrizability.

Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	981-4571-51-2 / 9814571512
ISBN-13	978-981-4571-51-7 / 9789814571517
Zustand	Neuware