On some properties of squares of Sierpiński sets
Volume 99 / 2004
Colloquium Mathematicum 99 (2004), 221-229
MSC: Primary 03E15; Secondary 03E20, 28E15.
DOI: 10.4064/cm99-2-7
Abstract
We investigate some geometrical properties of squares of special Sierpiński sets. In particular, we prove that (under CH) there exists a Sierpiński set $S$ and a function $p \colon \kern .16667em S \to S$ such that the images of the graph of this function under $\pi ^{\prime }(\langle x, y\rangle ) = x - y$ and $\pi ^{\prime \prime }(\langle x, y\rangle ) = x + y$ are both Lusin sets.
