ABSTRACT
The Stone Cech compactification of a space is of interest at least in part because it has nice properties with respect to extension of functions. Every bounded continuous real-valued function on a space extends continuously over its Stone-Cech compactification. It would be nice, therefore, to find compactifications of spaces which steer a middle course - compactifications which have some of the extension properties of the Stone-Cech compactification and yet which have a simpler structure. This chapter presents examples of spaces admitting various kinds of compactifications. It discusses ways of getting compactifications which contain no points of the Stone-Cech remainder of a space and some of the function-extension properties of the Stone-Cech compactification. In the process, the chapter answers some questions of A. Berner.
