In mathematics, specifically in order theory and functional analysis, if
is a cone at 0 in a vector space
then a subset
{\displaystyle [S]_{C}:=(S+C)\cap (S-C).}
Given a subset
-saturated hull of
is the smallest
-saturated subset of
that contains
is a collection of subsets of
is a collection of subsets of
is a subset of
is a fundamental subfamily of
is contained as a subset of some element of
is a family of subsets of a TVS
then a cone
is called a
is a fundamental subfamily of
is a strict
is a fundamental subfamily of
-saturated sets play an important role in the theory of ordered topological vector spaces and topological vector lattices.
is an ordered vector space with positive cone
[1] The map
is increasing; that is, if
is convex then so is
is considered as a vector field over
is balanced then so is
is a filter base (resp.
a filter) in
then the same is true of