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- W2886010524 abstract "It is well-known that Hausdorff dimension is not a topological invariant; that is, that two homeomorphic continua can have different Hausdorff dimension, although their topological dimension will be equal. We show that it is possible to take any continuum embeddable in $mathbb{R}^n$ and embed it in such a way that its Hausdorff dimension is $n$. In doing so, we can obtain an arbitrarily high Hausdorff dimension for any nondegenerate continuum. As an example, we will give different embeddings of an arc whose Hausdorff dimension is any real number between $1$ and $infty$, including an arc of infinite Hausdorff dimension." @default.
- W2886010524 created "2018-08-22" @default.
- W2886010524 creator A5037686752 @default.
- W2886010524 date "2018-05-01" @default.
- W2886010524 modified "2023-09-26" @default.
- W2886010524 title "Arbitrarily High Hausdorff Dimensions of Continua" @default.
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- W2886010524 doi "https://doi.org/10.35834/mjms/1534384956" @default.
- W2886010524 hasPublicationYear "2018" @default.
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