Geodesic
On some properties of squares of Sierpiński sets
Andrzej Nowik1
1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland and Faculty of Applied Physics and Mathematics Technical University of Gdańsk Gabriela Narutowicza 11/12 80-952 Gdańsk, Poland
Colloquium Mathematicum, Tome 99 (2004) no. 2, pp. 221-229

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm99-2-7
Keywords: investigate geometrical properties squares special sierpi ski sets particular prove under there exists sierpi ski set function colon kern images graph function under prime langle rangle prime prime langle rangle lusin sets

Andrzej Nowik 1

1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland and Faculty of Applied Physics and Mathematics Technical University of Gdańsk Gabriela Narutowicza 11/12 80-952 Gdańsk, Poland 
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Andrzej Nowik. On some properties of squares of Sierpiński sets. Colloquium Mathematicum, Tome 99 (2004) no. 2, pp. 221-229. doi: 10.4064/cm99-2-7

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