In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these investigated. It is shown that quotient sublattices g-supplemented. If 〖{a_i/0} 〗_(i∈I) a collection L 1=⋁_(i∈I) a_i, then also proved without loss generality weak g-supplements cofinite elements in compactly generated compact. An example showing not true for which given. A condition given under lat...