EN
For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series $∑_{n=1}^{∞} x(n)$. Guthrie and Nymann proved that E(x) is one of the following types of sets: (𝓘) a finite union of closed intervals; (𝓒) homeomorphic to the Cantor set; 𝓜 𝓒 homeomorphic to the set T of subsums of $∑_{n=1}^{∞} b(n)$ where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, 𝓒 and 𝓜 𝓒 the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), (𝓒) and (𝓜 𝓒), respectively. We show that ℐ and 𝓒 are strongly 𝔠-algebrable and 𝓜 𝓒 is 𝔠-lineable. We also show that 𝓒 is a dense $𝒢_δ$-set in ℓ₁ and ℐ is a true $ℱ_σ$-set. Finally we show that ℐ is spaceable while 𝓒 is not.