Convergence Foundations of Topology

This book is informed by the past 15 years of my research on convergence spaces and that of my mentor, friend and collaborator Szymon Dolecki. It offers an original convergence-centered viewpoint on the material classically covered in an introductory Point-set Topology text, while gathering for the first time in book format a wealth of results on convergence spaces so far scattered through the literature.

From the publisher: "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.

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 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."

The book has been well-received so far: from the MAA review: "It is clear that the book, with its high level of scholarship, is a labor 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."

World Scientific's webpage for the book will also maintain supplements as they become available. In particular, we are preparing a booklet with solutions of the exercises, supplemental exercises, errata and complements.

Please use this page to order the book or recommend it to your library. For a limited time, you can receive a 20% discount with code WSMTH1220.