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Stably compact spaces

Published online by Cambridge University Press:  15 September 2010

JIMMIE LAWSON
JIMMIE LAWSON*
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. Email: lawson@math.lsu.edu
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Abstract

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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:

  1. (i) the property of stable compactness is preserved under a large variety of constructions involving powerdomains, hyperspaces and function spaces;

  2. (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

  3. (iii) the notion of inner and outer pavings is a useful and natural tool for such studies of stably compact spaces.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 1 , February 2011 , pp. 125 - 169
Copyright
Copyright © Cambridge University Press 2010

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