Convergence Foundations Of Topology

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Szymon Dolecki (Univ Of Burgundy, France) Frederic Mynard (New Jersey City Univ, Usa)

Convergence Foundations Of Topology

Szymon Dolecki (Univ Of Burgundy, France), Frederic Mynard (New Jersey City Univ, Usa)

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English

World Scientific Publishing Co Pte Ltd
16 May 2016

Topology

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.

By: Szymon Dolecki (Univ Of Burgundy France), Frederic Mynard (New Jersey City Univ, Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Dimensions: Height: 234mm, Width: 157mm, Spine: 33mm
Weight: 953g
ISBN: 9789814571517
ISBN 10: 9814571512
Pages: 568
Publication Date: 16 May 2016
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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