In mathematics, specifically in order theory and functional analysis, a filter in an order complete vector lattice X is order convergent if it contains an order bounded subset (i.e. is contained in an interval of the form [a,b] = { x ∈ X : a ≤ x ≤ b }) and if , , where is the set of all order bounded subsets of X, in which case this common value is called the order limit of (in X). Order convergence plays an important role in the theory of vector lattices because the definition of order convergence does not depend on any topology.