A remark on singularity of homeomorphisms and Hausdorff dimension

Authors : Chun Wei, Shengyou Wen

Pages : 784-788

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Publication Date : 9999-12-31

Article Type : Makaleler

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