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Journal of Applied Analysis 9 (2003), No. 2, 275--286
Copyright Heldermann Verlag 2003
On Marczewski-Burstin Representations of Algebras and Ideals
Marek Balcerzak
Faculty of Mathematics, University of Lodz, Banacha 22, 90-238 Lodz, Poland,
mbalce@uni.lodz.pl
Joanna Rzepecka
Institute of Mathematics, Technical University, Al. Politechniki 11, 90-924 Lodz, Poland
We study MB-representations of algebras and ideals when they are relativized to a
subset, and when one considers the operations of sum and intersection for families of
algebras and ideals. We observe that the algebras Δα0,
3 ≤ α < ω1, on R are MB-representable under GCH.
We find a class of topological spaces in which the algebra of clopen sets is MB-representable.
Keywords: Marczewski operation, sums of algebras of sets, ambiguous Borel sets, clopen
sets.
MSC 2000: 54H05, 06E25, 03E15.
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