Convergence Foundations of Topology

This textbook is an alternative to a classical introductory book in point-set topology.

Convergence Foundations of 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.

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Convergence Foundations of Topology
Language: en
Pages: 568
Authors: Szymon Dolecki, Frédéric Mynard
Categories: Mathematics
Type: BOOK - Published: 2016-05-13 - Publisher: World Scientific Publishing Company

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
Convergence Foundations of Topology
Language: en
Pages:
Authors: Szymon Dolecki
Categories: Mathematics
Type: BOOK - Published: 2016 - Publisher:

Books about Convergence Foundations of Topology
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Categories: Mathematics
Type: BOOK - Published: 2014-05-12 - Publisher: Academic Press

Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents
Foundations of Topology
Language: en
Pages: 303
Authors: Gerhard Preuß
Categories: Mathematics
Type: BOOK - Published: 2011-06-27 - Publisher: Springer Science & Business Media

A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In
Foundations of Topology
Language: en
Pages: 380
Authors: C. Wayne Patty
Categories: Computers
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Topology is a branch of pure mathematics that deals with the abstract relationships found in geometry and analysis. Written with the mature student in mind, Foundations of Topology, Second Edition, provides a user-friendly, clear, and concise introduction to this fascinating area of mathematics. The author introduces topics that are well-motivated