A note on monotonically normal spaces.

We show that a monotonically normal space X is paracompact if and only if for every increasing open cover { U α : α < κ} of X, there is a closed cover { F nα : n < ω, α < κ} of X such that F nα ⊂ U α for n < ω, α < κ and F nα ⊂ F nβ if α ≦ β. [ABSTRACT FROM AUTHOR]