On some properties of squares of Sierpiński sets

Tom 99 / 2004

Andrzej Nowik Colloquium Mathematicum 99 (2004), 221-229 MSC: Primary 03E15; Secondary 03E20, 28E15. DOI: 10.4064/cm99-2-7

Streszczenie

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.

Autorzy

  • Andrzej NowikInstitute 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
    e-mail
    e-mail

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