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

DOI

10.3906/mat-1501-34

Keywords

Singularity, homeomorphism, Hausdorff dimension

First Page

784

Last Page

788

Recommended Citation

WEI, CHUN and WEN, SHENGYOU (2016) "A remark on singularity of homeomorphisms and Hausdorff dimension," Turkish Journal of Mathematics: Vol. 40: No. 4, Article 7. https://doi.org/10.3906/mat-1501-34
Available at: https://journals.tubitak.gov.tr/math/vol40/iss4/7