Visualizing paradoxical sets (Q483351)

This paper shows how several counterintuitive ideas of set theory, such as the Banach-Tarski paradox and the existence of a certain type of Sierpiński set, can be given concrete interpretations in the hyperbolic plane. The authors use the upper-half plane model of hyperbolic geometry and the Poincaré disk model. The article ends with a conjecture which states that there is no discrete weak Sierpiński set in \(\mathbb R^3\).