The closed neighborhood and filter conditions in solid sequence spaces - P. D. Johnson, Jr. (International Journal of Mathematics and Mathematical Sciences)
Let E be a topological vector space of scalar sequences, with topology τ; (E,τ) satisfies the closed neighborhood condition iff there is a basis of neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect to the topology π of coordinate-wise convergence on E; (E,τ) satisfies the filter condition iff every filter, Cauchy with respect to τ, convergent with respect to π, converges with respect to τ.