On the connected components of fractal cubes

Dmitry Drozdov; Andrei Tetenov

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arXiv · 2002.02920

On the connected components of fractal cubes

Dmitry Drozdov·Andrei Tetenov

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Abstract

We show that a fractal cube $F$ in $\mathbb R^3$ may have an uncountable set $Q$ of connected components $K_α$ neither of which is contained in any plane, whereas the set $Q$ is a totally disconnected self-similar subset of the hyperspace $C(\mathbb R^3)$, isomorphic to a Cantor set.

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BibTeX RIS

Dmitry Drozdov, Andrei Tetenov. 2020-02-07. On the connected components of fractal cubes. https://arxiv.org/abs/2002.02920

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