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  • On coabsolute paracompact spaces

  • Part of
  • Catherine L. Gates
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics / Volume 27 / Issue 2 / March 1979
    Published online by Cambridge University Press:
    09 April 2009, pp. 248-256
    Print publication:
    March 1979
    • Article
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  • We are interested in determining whether two spaces are coabsolute by comparing their Boolean algebras of regular closed sets. It is known that when the spaces are compact Hausdorff they are coabsolute precisely when the Boolean algebras of regular closed sets are isomorphic; but in general this condition is not strong enough to insure that the spaces be coabsolute. In this paper we show that for paracompact Hausdorff spaces, the spaces are coabsolute when the Boolean algebra isomorphism and its inverse ‘preserve’ local finiteness, and for locally compact paracompact Hausdorff spaces, the spaces are coabsolute when the collections of compact regular closed subsets are ‘isomorphic’.