PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On dense subsets in spaces of metrics

Volume 170 / 2022

Yoshito Ishiki Colloquium Mathematicum 170 (2022), 27-39 MSC: Primary 54E45; Secondary 30L05. DOI: 10.4064/cm8580-9-2021 Published online: 13 April 2022


In spaces of metrics, we investigate topological distributions of the doubling property, uniform disconnectedness, and uniform perfectness, which are quasi-symmetrically invariant properties appearing in the David–Semmes theorem. We show that the set of all doubling metrics and the set of all uniformly disconnected metrics are dense in spaces of metrics on finite-dimensional and zero-dimensional compact metrizable spaces, respectively. Conversely, this denseness implies the finite-dimensionality, zero-dimensionality, and compactness of metrizable spaces. We also determine the topological distribution of the set of all uniformly perfect metrics in the space of metrics on the Cantor set.


  • Yoshito IshikiGraduate School of Pure and Applied Sciences
    University of Tsukuba
    Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8571, Japan
    Current address:
    Photonics Control Technology Team
    RIKEN Center for Advanced Photonics
    2-1 Hirasawa, Wako, Saitama 351-0198, Japan

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image