# Absolutely convex set

A set *C* in a real or complex vector space is said to be **absolutely convex** or **disked** if it is convex and balanced (circled), in which case it is called a **disk**.

## Properties

A set is absolutely convex if and only if for any points in and any numbers satisfying the sum belongs to .

Since the intersection of any collection of absolutely convex sets is absolutely convex then
for any subset *A* of a vector space one can define its **absolutely convex hull**
to be the intersection of all absolutely convex sets containing *A*.

## Absolutely convex hull

The absolutely convex hull of the set *A* assumes the following representation

.

## See also

The Wikibook Algebra has a page on the topic of: Vector spaces |

- vector (geometric), for vectors in physics
- Vector field

## References

- Robertson, A.P.; W.J. Robertson (1964).
*Topological vector spaces*. Cambridge Tracts in Mathematics.**53**. Cambridge University Press. pp. 4–6. - Narici, Lawrence; Beckenstein, Edward (July 26, 2010).
*Topological Vector Spaces, Second Edition*. Pure and Applied Mathematics (Second ed.). Chapman and Hall/CRC.

- Schaefer, H.H. (1999).
*Topological vector spaces*. Springer-Verlag Press. p. 39.

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