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.


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 light gray area is the Absolutely convex hull of the cross.

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


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