Saturated family

In mathematics, specifically in functional analysis, a family of subsets a topological vector space (TVS) is said to be saturated if contains a non-empty subset of and if for every the following conditions all hold: 1. * contains every subset of ; 2. * the union of any finite collection of elements of is an element of ; 3. * for every scalar contains ; 4. * the closed convex balanced hull of belongs to rdf:langString