Locally convex vector lattice
Appearance
In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space.[1] LCVLs are important in the theory of topological vector lattices.
Properties
Every locally convex vector lattice possesses a neighborhood base at the origin consisting of convex balanced solid absorbing sets.[1]
Examples
Every Banach lattice, normed lattice, and Fréchet lattice is a locally convex vector lattice.
See also
References
- ^ a b Schaefer 1999, pp. 234–242.