Abstract
Abstract We introduce the notion of K-ideals associated with Kuratowski partitions. Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal.
Highlights
We introduce the notion of K-ideals associated with Kuratowski partitions
Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal
The main idea of this paper is to show some operations on complete ideals associated with so called Kuratowski partitions
Summary
The main idea of this paper is to show some operations on complete ideals associated with so called Kuratowski partitions. It requires using some properties of topology of given spaces for which the Kuratowski partitions and these ideals exist. With any Kuratowski partition of a topological space into meager sets we associate an ideal called in this paper a K-ideal (see Section 2 for the formal de nition). It seemed that the knowledge of such K-ideal could help to determine whether a given space admits Kuratowski partition. The motivation for consideration an incomplete metric Baire space with Kuratowski partition comes from [5], where the authors consider the existence of such partitions for complete and incomplete metric Baire spaces
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