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Jan 21, 2019 at 11:33 comment added Taras Banakh It is well-known that a compact metric space $X$ admits a continuous injection into some Euclidean space if and only if $X$ has finite topological dimension. More precesely, each metrizable separable space $X$ of finite dimension $n$ admits a topological embedding to the Euclidean space $\mathbb R^{2n+1}$.
Jan 21, 2019 at 9:29 comment added ABIM A typo... now it's Euclidean space.
Jan 21, 2019 at 9:28 history edited ABIM CC BY-SA 4.0
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Jan 21, 2019 at 8:46 history asked ABIM CC BY-SA 4.0