Partitions of non-complete Baire metric spaces

TL;DR

This paper explores the properties of ideals linked to Kuratowski partitions in non-complete Baire metric spaces, demonstrating that such ideals can possess the precipitous property, which has implications in topology and set theory.

Contribution

It introduces the possibility that ideals associated with Kuratowski partitions in non-complete Baire metric spaces can be precipitous, expanding understanding of their structural properties.

Findings

Ideals associated with Kuratowski partitions can be precipitous.

Non-complete Baire metric spaces admit such ideals with special properties.

The study advances the theory of ideals in topological spaces.

Abstract

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.