The gap between the dimensions of countably paracompact spaces

摘要

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.