The gap between the dimensions of countably paracompact spaces

Let l , m , n be integers such that 0 ⩽ l ⩽ n and 0 < m ⩽ n . We show that there is a first countable, separable, ω 1 -compact, countably paracompact and normal space X l , m , n with ind X l , m , n = l , dim X l , m , n = m and Ind X l , m , n = n and point out some interesting questions concerning the gap between the dimensions of paracompact spaces.