Cone-saturated

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