位相幾何学の収束的基礎（テキスト） Convergence Foundations of Topology

Dolecki, Szymon/ Mynard, Frederic

World Scientific Publishing Co Pte Ltd（2016/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 568 p.
• 言語 ENG
• 商品コード 9789814571524
• DDC分類 514

Full Description

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.

Contents

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