Partitions of non-complete Baire metric spaces
We investigate the properties of ideals associated with Kuratowski partitions of non-complete Baire metric spaces. We show that such an ideal can be precipitous.
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arXiv subjects
Joanna Jureczko
Publications and source records attributed to Joanna Jureczko.
On Kuratowski partitions in the Marczewski structure and Ellentuck topology
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.
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A short mathematical proof of Frankiewicz - Kunen theorem
In this paper there is proved without any metamathematical techniques that the existence of precipitous ideals immediately follows from Kuratowski partitions.
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Some remarks on Kuratowski partitions
We introduce the notion of $K$-ideals associated with Kuratowski partitions and we prove that each $κ$-complete ideal on a measurable cardinal $κ$ can be represented as a $K$-ideal. Moreover, we show some results concerning precipitous and Fréchet ideals.
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On Kuratowski partitions
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 property, is continuous apart from a meager set. This paper is a selection of older results related to the question posed by Kuratowski in 1935, coming from among others Solovay and Bukovsk?y, and quite new ones concerning considerations in Ellentuck topology and some propertiesof K-ideals, (i.e. ideals associated with Kuratowski partitions).
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