Fréchet lattice


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

Properties

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

Examples

Every Banach lattice is a Fréchet lattice.