
Radial set
Encyclopedia
In mathematics, given a linear space
, a set
is radial at the point
if for every
there exists a
such that for every
,
. In set notation,
is radial at the point
if
The set of all points at which
is radial is equal to the algebraic interior
.
A set
is absorbing
if and only if it is radial at 0.










The set of all points at which

Algebraic interior
In functional analysis, a branch of mathematics, the algebraic interior or radial kernel of a subset of a vector space is a refinement of the concept of the interior. It is the subset of points contained in a given set that it is absorbing with respect to, i.e...
.
A set

Absorbing set
In functional analysis and related areas of mathematics an absorbing set in a vector space is a set S which can be inflated to include any element of the vector space...
if and only if it is radial at 0.