Stably compact spaces

The purpose of this paper is to develop the basic theory of stably compact spaces (viz. compact, locally compact, coherent sober spaces) and introduce in an accessible manner and with a minimum of prerequisites some significant new lines of investigation and application arising from recent research, which has arisen primarily in the theoretical computer science community. Three primary themes have developed: (i) the property of stable compactness is preserved under a large variety of constructions involving powerdomains, hyperspaces and function spaces; (ii) the underlying de Groot duality of stably compact spaces, which finds varied expression, is reflected by duality theorems involving the just mentioned constructions; and (iii) the notion of inner and outer pavings is a useful and natural tool for such studies of stably compact spaces.