Convergence foundations of topology (Q2812996)

This book presents the basic notions of topology as a particular case of convergence spaces. Hence, it also can be considered as a first course in foundations of analysis. The convergence of filters is a natural generalization of the well-known concept of convergence of sequences, but as framework much more easier to handle. Consequently, topological spaces are presented as a special subclass of convergence spaces, and most of the material usually developed in a text book concerning topology is treated in this larger realm of convergence. An appendix of basic set theory is added, and most of the treated statements of this book are supported by corresponding examples without solutions. These are given in a companion document available on the book's website at \url{http://www.worldscientific.com/worldscibooks/10.1142/9012}. Moreover the book also can serve as a useful reference for mathematicians, working in analysis and topology, respectively, and it is closed by some important historical remarks.