ℓ₁(κ) admits no tiling by balls for κ < 2^ℵ₀, including the case of ℓ₁ itself.
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Tilings and coverings by balls in $\ell_1$
ℓ₁(κ) admits no tiling by balls for κ < 2^ℵ₀, including the case of ℓ₁ itself.