A solution to the problem of the existence of a dense plastic subset $X\subseteq \mathbb{R}$ of cardinality $|X|<\mathfrak{c}$

Abstract

Under the assumption $\mathfrak{c}⩾{\omega }_2$, we give an example of a dense plastic subset $X\subseteq \mathbb{R}$ of cardinality $|X|<\mathfrak{c}$. This answers Problem 1 of arXiv:2510.10537.