Fractal dimensions in the Gromov–Hausdorff space

• Autorzy: Ishiki Yoshito

Identyfikatory

DOI

10.4064/ba221212-16-11

• Języki publikacji: EN

Abstrakty

EN

We first show that for any four non-negative real numbers, there exists a Cantor ultrametric space whose Hausdorff dimension, packing dimension, upper box dimension, and Assouad dimension are equal to the given four numbers, respectively. Next, using a direct sum of metric spaces, we construct topological embeddings of an arbitrary compact metrizable space into the two subsets of the Gromov–Hausdorff space: the set of all compact metric spaces possessing prescribed topological dimension and the aforementioned four dimensions, and the set of all compact ultrametric spaces.

Słowa kluczowe

EN

fractal dimension; Gromov–Hausdorff distance

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2023
• Tom: Vol. 71, no 2
• Strony: 147--168
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Ishiki Yoshito

• Photonics Control Technology Team, RIKEN Center for Advanced Photonics Wako, Saitama 351-0198, Japan

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024)