A remark on singularity of homeomorphisms and Hausdorff dimension

Authors: CHUN WEI, SHENGYOU WEN

Abstract: We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set $E$ of $\dim_HE=0$ onto a set $F$ of $\dim_H[0,1]\setminus F=0$.

Keywords: Singularity, homeomorphism, Hausdorff dimension

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