# Some remarks on Kuratowski partitions

## TL;DR

This paper introduces $K$-ideals linked to Kuratowski partitions, demonstrating their representation of $ ext{kappa}$-complete ideals on measurable cardinals and exploring properties of precipitous and Fréchet ideals.

## Contribution

It defines $K$-ideals for Kuratowski partitions and proves their correspondence with $ ext{kappa}$-complete ideals on measurable cardinals, advancing understanding of ideal structures.

## Key findings

- Each $ ext{kappa}$-complete ideal on a measurable cardinal can be represented as a $K$-ideal.
- Results on precipitous and Fréchet ideals are established.
- New connections between Kuratowski partitions and ideal theory are demonstrated.

## Abstract

We introduce the notion of $K$-ideals associated with Kuratowski partitions and we prove that each $\kappa$-complete ideal on a measurable cardinal $\kappa$ can be represented as a $K$-ideal. Moreover, we show some results concerning precipitous and Fr\'echet ideals.