# Convergence Foundations of Topology

## Document Type

Book

## Publication Date

2009

## Publication Title

Convergence Foundations of Topology

## ISBN

9789814571524

## Abstract

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).

## Recommended Citation

Dolecki, Szymon, Frédéric D. Mynard.
2009.
"Convergence Foundations of Topology."
*Convergence Foundations of Topology*: World Scientific Publishers.
isbn: 9789814571524

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/278