Article contents
An unpleasant set in a non-locally-convex vector lattice
Published online by Cambridge University Press: 20 January 2009
Extract
In a linear topological space E one often carries out various “ smoothing ” operations on a subset A, such as taking the convex hull co A and the closure A-. If E is also a (real) vector lattice, the solid hull
is also a natural “ smoothing out ” of A. If sol A = A then A is called solid, and if E has a base of solid neighbourhoods of 0 as do all the common topological vector lattices such as C(X), Lp, Köthe spaces and so on—then E is called a locally solid space.
- Type
- Research Article
- Information
- Copyright
- Copyright © Edinburgh Mathematical Society 1973
References
REFERENCES
- 2
- Cited by