In
mathematics, a subset
of a
linear space is radial at a given point
if for every
there exists a real
such that for every
Geometrically, this means
is radial at
if for every
there is some (non-degenerate) line segment (depend on
) emanating from
in the direction of
that lies entirely in
Every radial set is a
star domain although not conversely.
Relation to the algebraic interior
The points at which a set is radial are called .
The set of all points at which
is radial is equal to the
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.
Definition
Assume that A is a subset of a vector space X.
The ''algebraic in ...
.
Relation to absorbing sets
Every
absorbing subset is radial at the origin
and if the vector space is real then the converse also holds. That is, a subset of a real vector space is
absorbing if and only if it is radial at the origin.
Some authors use the term ''radial'' as a synonym for ''
absorbing''.
See also
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References
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{{topology-stub
Convex analysis
Functional analysis
Linear algebra
Topology