In mathematics, specifically in functional analysis, a family
of subsets a topological vector space (TVS)
then the smallest saturated family containing
is called the saturated hull of
; it is total if the linear span of this set is a dense subset of
[1] The intersection of an arbitrary family of saturated families is a saturated family.
is saturated, any given non-empty family
containing at least one non-empty set, the saturated hull of
[2] Note that a saturated family of subsets of
The set of all bounded subsets of a topological vector space is a saturated family.