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Oct 2, 2022 at 3:02 comment added Saúl RM What could be an idea to create the injective curve $\gamma:[0,1]\to\mathbb{R}^2$ from the first paragraph while making sure that it is still continuous? Specifically, how can we make sure that, if $(a_n,b_n)$ are the connected components of the complement of the Cantor set, then the diameter of $\gamma((a_n,b_n))$ tends to $0$ when $n\to\infty$?
Oct 1, 2022 at 16:04 history edited Piotr Hajlasz CC BY-SA 4.0
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Oct 1, 2022 at 11:51 history edited Piotr Hajlasz CC BY-SA 4.0
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Sep 30, 2022 at 22:04 history edited Piotr Hajlasz CC BY-SA 4.0
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Sep 30, 2022 at 16:00 history answered Piotr Hajlasz CC BY-SA 4.0