4 papers
On Kuratowski partitions
Ryszard Frankiewicz, Joanna Jureczko
In 1935 K. Kuratowski posed the problem whether a function f:X ! Y , (X is completely metrizable and Y is metrizable), with the property that a preimage of each open has the Baire…
A short mathematical proof of Frankiewicz - Kunen theorem
Ryszard Frankiewicz, Joanna Jureczko
In this paper there is proved without any metamathematical techniques that the existence of precipitous ideals immediately follows from Kuratowski partitions.
On Kuratowski partitions in the Marczewski structure and Ellentuck topology
Ryszard Frankiewicz, Joanna Jureczko
We show that large sets in Ellentuck topology (i.e. sets which are not nowhere Ramsey) do not admit Kuratowski's partition. The similar result is true for the Sacks real forcing.
Remarks on quotient algebras
Ryszard Frankiewicz, Sławomir Szczepaniak
The structure of quotient Boolean algebras in terms of cardinal invariants is investigated. Some results of Gitik and Shelah regarding atomless ideals are reproved and proofs are s…