In mathematics, specifically in order theory and functional analysis, a normed lattice is a topological vector lattice that is also a normed space whose unit ball is a solid set.
[1] Normed lattices are important in the theory of topological vector lattices.
They are closely related to Banach vector lattices, which are normed vector lattices that are also Banach spaces.
[1] The strong dual of a normed lattice is a Banach lattice with respect to the dual norm and canonical order.
If it is also a Banach space then its continuous dual space is equal to its order dual.