# Radial set

In mathematics, given a linear space
, a set
is **radial** at the point
if for every
there exists a
such that for every
,
.[1] Geometrically, this means
is radial at
if for every
a line segment emanating from
in the direction of
lies in
, where the length of the line segment is required to be non-zero but can depend on
.

The set of all points at which is radial is equal to the algebraic interior.[1][2] The points at which a set is radial are often referred to as internal points.[3][4]

A set
is absorbing if and only if it is radial at 0.[1] Some authors use the term *radial* as a synonym for *absorbing*, i. e. they call a set radial if it is radial at 0.[5]

## References

- Jaschke, Stefan; Küchler, Uwe (2000). "Coherent Risk Measures, Valuation Bounds, and (
)-Portfolio Optimization". Cite journal requires
`|journal=`

(help) - Nikolaĭ Kapitonovich Nikolʹskiĭ (1992).
*Functional analysis I: linear functional analysis*. Springer. ISBN 978-3-540-50584-6. - Aliprantis, C.D.; Border, K.C. (2007).
*Infinite Dimensional Analysis: A Hitchhiker's Guide*(3 ed.). Springer. pp. 199–200. doi:10.1007/3-540-29587-9. ISBN 978-3-540-32696-0. - John Cook (May 21, 1988). "Separation of Convex Sets in Linear Topological Spaces" (pdf). Retrieved November 14, 2012.
- Schaefer, Helmuth H. (1971).
*Topological vector spaces*. GTM.**3**. New York: Springer-Verlag. ISBN 0-387-98726-6.

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