Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Variants of Compactness in Pointfree Topology

  • Banaschewski, Bernhard (Department of Mathematics and Statistics, McMaster University) ;
  • Hong, Sung Sa (Department of Mathematics, Sogang University)
  • Received : 2005.09.06
  • Published : 2005.12.23
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Abstract

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

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References

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