Stably compact spaces

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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. © 2010 Cambridge University Press.

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Mathematical Structures in Computer Science

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