On non-Baire rare sets in category bases

TL;DR

This paper investigates non-Baire rare sets within category bases that form an -independent family, generalizing Luzin and Sierpinski sets, and explores their properties.

Contribution

It introduces the concept of non-Baire rare sets in category bases and examines their structure within -independent families, extending classical set theory concepts.

Findings

Non-Baire rare sets are characterized within -independent category bases.

The paper generalizes classical Luzin and Sierpinski sets.

Properties of these rare sets are analyzed in the context of category bases.

Abstract

In this paper, we deal with non-Baire rare sets in category bases which forms $\aleph_0$-independent family, where a rare set is a common generalization of both Luzin and Sierpinski set.