We defined the ℓ p , q -summability property and study the relations between the ℓ p , q -summability property, the Banach-Mackey spaces and the locally complete spaces.
We prove that, for c 0 -quasibarrelled spaces, Banach-Mackey and locally complete are equivalent. Last section is devoted to the study of CS-closed sets introduced by Jameson and Kakol.