Convergence Foundations Of Topology by Szymon Dolecki (PDF)

Description

“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.

User’s Reviews

Editorial Reviews: From the Back Cover The 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. On the one hand, 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. Topology spaces are introduced 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. A number of exercises (with solutions) form an essential part of the text. Additional problems for each chapter are included (without solutions).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐An amazing book to learn about topology from the convergence viewpoint. I continue to learn new things whenever I get the chance to go back and reread any section from it. I highly recommend it to anyone interested to learn and study Topology within the larger context of Convergence Spaces and Convergences Theory.

⭐

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