# On Kuratowski partitions in the Marczewski structure and Ellentuck topology

## TL;DR

This paper proves that large sets in Ellentuck topology and Sacks real forcing do not admit Kuratowski's partition, highlighting a structural limitation in these mathematical frameworks.

## Contribution

It establishes the non-existence of Kuratowski's partitions for large sets in Ellentuck topology and Sacks real forcing, extending understanding of their combinatorial properties.

## Key findings

- Large sets in Ellentuck topology do not admit Kuratowski's partition.
- The same non-admission result holds for sets in Sacks real forcing.
- Provides new insights into the structure of large sets in descriptive set theory.

## Abstract

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.