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 $\dim_H[0,1]\setminus F=0$.

DOI

10.3906/mat-1501-34

Keywords

Singularity, homeomorphism, Hausdorff dimension

First Page

784

Last Page

788

Recommended Citation

WEI, C, & WEN, S (2016). A remark on singularity of homeomorphisms and Hausdorff dimension. Turkish Journal of Mathematics 40 (4): 784-788. https://doi.org/10.3906/mat-1501-34

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