In mathematics, given a linear space
X
, a set
A
⊆
X
is radial at the point
x
0
∈
A
if for every
x
∈
X
there exists a
t
x
>
0
such that for every
t
∈
[
0
,
t
x
]
,
x
0
+
t
x
∈
A
. Geometrically, this means
A
is radial at
x
0
if for every
x
∈
X
a line segment emanating from
x
0
in the direction of
x
lies in
A
, where the length of the line segment is required to be non-zero but can depend on
x
.
The set of all points at which
A
⊆
X
is radial is equal to the algebraic interior. The points at which a set is radial are often referred to as internal points.
A set
A
⊆
X
is absorbing if and only if it is radial at 0. Some authors use the term radial as a synonym for absorbing, i. e. they call a set radial if it is radial at 0.
