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ArticleOriginal scientific text

Title

The sequential topology on complete Boolean algebras

Authors 1, 2, 3

Affiliations

  1. Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
  2. Mathematical Institute of the Academy of Sciences of Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
  3. Department of Mathematics, The Pennsylvania State University, 218 McAllister Bldg., University Park, Pennsylvania 16802, U.S.A.

Abstract

We investigate the sequential topology τs on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the space (B,τs) is Hausdorff. We also characterize sequential cardinals.

Keywords

ENG
complete Boolean algebra, sequential topology, Maharam submeasure, sequential cardinal

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Fundamenta Mathematicae
1998/155/1
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Pages:
59-78
Main language of publication
English
Received
1996-12-17
Published
1998
Exact and natural sciences