Absolutely convex set
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
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- 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.