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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