Recent research has produced a large number of results concerning
the Stone-Cech compactification or involving it in a central
manner. The goal of this volume is to make many of these results
easily accessible by collecting them in a single source together
with the necessary introductory material. The author's interest in
this area had its origin in his fascination with the classic text
Rings of Continuous Functions by Leonard Gillman and Meyer Jerison.
This excellent synthesis of algebra and topology appeared in 1960
and did much to draw attention to the Stone-Cech compactification
{3X as a tool to investigate the relationships between a space X
and the rings C(X) and C*(X) of real-valued continuous functions.
Although in the approach taken here {3X is viewed as the object of
study rather than as a tool, the influence of Rings of Continuous
Functions is clearly evident. Three introductory chapters make the
book essentially self-contained and the exposition suitable for the
student who has completed a first course in topology at the
graduate level. The development of the Stone Cech compactification
and the more specialized topological prerequisites are presented in
the first chapter. The necessary material on Boolean algebras,
including the Stone Representation Theorem, is developed in Chapter
2. A very basic introduction to category theory is presented in the
beginning of Chapter 10 and the remainder of the chapter is an
introduction to the methods of categorical topology as it relates
to the Stone-Cech compactification."
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