Fréchet lattice

From HandWiki

In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space.[1] Fréchet lattices are important in the theory of topological vector lattices.

Properties

Every Fréchet lattice is a locally convex vector lattice.[1] The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.[1]

Examples

Every Banach lattice is a Fréchet lattice.

See also

References

  1. 1.0 1.1 1.2 Schaefer & Wolff 1999, pp. 234–242.

Bibliography