On Drop Property In Locally Convex Seperated Space

First ,we defined the T drop property and quasi T drop property for the closed bounded convex in locally convex separated space(lcs) (X,T).1) we discusse the heredity of the drop property and weak drop property in Banach space.2) Let (X,T) is a Frechet space and B is a closed bounded convex set. T₁ is comparable with T, then: B has T₁ drop property if and only if the stream of the set B has a T₁ convergent subsequence and B has quasi T₁ drop property if and only if the set of the stream of the set B has a T₁ cluster point3) Every sequentially compact closed convex set in the lcs (X,T) has T drop property and every countable compact set has quasi T drop property.Second, we have discussed the locally cauchy sequence, locally complete and locally drop property in lcs.1) Let (X,T) is lcs, then sequence (x_n)is locally cauchy sequence if and only if there is an increasing unbounded sequence of positive real numbers (a_n) such that 2) There is some condition of equivalency for the locally complete of the lcs.3) Locally sequence compact and locally drop property is introduced and locally sequence compact implies the locally drop property.