The Replenishment Algorithm in Algebras of Sets

2021 ◽  
Author(s):  
M. Lvov ◽  
Y. Tarasich
Keyword(s):  
Algebras Of Sets

On Lower and Semi-Lower Density Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 661-671
Author(s):  
Jacek Hejduk ◽  
Anna Loranty
Keyword(s):  
Density Operator ◽  
Baire Property ◽  
Density Operators ◽  
Dense Sets ◽  
Meager Sets ◽  
Algebras Of Sets

Abstract This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

scholarly journals ON MARCZEWSKI-BURSTIN REPRESENTATIONS OF CERTAIN ALGEBRAS OF SETS

2000 ◽  
Vol 26 (2) ◽  
pp. 581 ◽  
Author(s):  
Balcerzak ◽  
Bartoszewicz ◽  
Ciesielski
Keyword(s):  
Algebras Of Sets

Algebras of sets generating non-barrelled spaces

1994 ◽  
Vol 29 (3) ◽  
pp. 207-211
Author(s):  
J. Ferrer ◽  
M. López-Pellicer
Keyword(s):  
Barrelled Spaces ◽  
Algebras Of Sets

scholarly journals Rainbow matchings and algebras of sets

2015 ◽  
Vol 49 ◽  
pp. 251-257
Author(s):  
Gabriel Nivasch ◽  
Eran Omri
Keyword(s):  
Algebras Of Sets

scholarly journals Algebras of Sets and Coherent Sets of Gambles

2021 ◽  
pp. 603-615
Author(s):  
Arianna Casanova ◽  
Juerg Kohlas ◽  
Marco Zaffalon
Keyword(s):  
Algebras Of Sets

Axiomatizing universal properties of quantifiers

1991 ◽  
Vol 56 (3) ◽  
pp. 901-905 ◽  
Author(s):  
Kees Doets
Keyword(s):  
Universal Properties ◽  
Algebras Of Sets

AbtractWe axiomatize all quantifier properties which can be expressed by a universal condition on the class of algebras of sets.

Maximal linked systems and ultrafilters: main representations and topological properties

2020 ◽  
pp. 68-84
Author(s):  
Aleksandr G. Chentsov
Keyword(s):  
Measurable Space ◽  
Topological Properties ◽  
Bitopological Space ◽  
Measurable Structure ◽  
Bitopological Spaces ◽  
Algebras Of Sets

Questions connected with representation of the ultrafilter (UF) set for widely understood measurable space are investigated; this set is considered as a subspace of bitopological space of maximal linked systems (MLS) under equipment with topologies of Wallman and Stone types (measurable structure is defined as a π -system with “zero” and “unit”). Analogous representations connected with generalized variant of cohesion is considered also; in this variant, for corresponding set family, it is postulated the nonemptyness of intersection for finite subfamilies with power not exceeding given. Conditions of identification of UF and MLS (in the above-mentioned generalized sense) are investigated. Constructions reducing to bitopological spaces with points in the form of MLS and 𝑛-supercompactness property generalizing the “usual” supercompactness are considered. Finally, some characteristic properties of MLS and their corollaries connected with the MLS contraction to a smaller π -system are being studied. The case of algebras of sets is selected separately.

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