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The sequential topology on complete Boolean algebras

100%
Główczyński W., Balcar B., Jech T. J.
Fundamenta Mathematicae
|
1998
|
tom 155
|
nr 1
59-78
EN
We investigate the sequential topology $τ_{s}$ 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 $(B,τ_{s})$ is Hausdorff. We also characterize sequential cardinals.
2
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On Todorcevic orderings

100%
Balcar B., Pazák T., Thümmel E.
Fundamenta Mathematicae
|
2015
|
tom 228
|
nr 2
173-192
EN
The Todorcevic ordering 𝕋(X) consists of all finite families of convergent sequences in a given topological space X. Such an ordering was defined for the special case of the real line by S. Todorcevic (1991) as an example of a Borel ordering satisfying ccc that is not σ-finite cc and even need not have the Knaster property. We are interested in properties of 𝕋(X) where the space X is taken as a parameter. Conditions on X are given which ensure the countable chain condition and its stronger versions for 𝕋(X). We study the properties of 𝕋(X) as a forcing notion and the homogeneity of the generated complete Boolean algebra.
3
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The space of ultrafilters on N covered by nowhere dense sets

100%
Balcar B., Pelant J., Simon P.
Fundamenta Mathematicae
|
1980
|
tom 110
|
nr 1
11-24
4
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Boolean matrices, subalgebras and automorphisms of complete Boolean algebras

99%
Balcar B., Štěpánek P.
Fundamenta Mathematicae
|
1977
|
tom 96
|
nr 3
211-223
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