On the relationship between cmp and def for separable metrizable spaces

For each pair of positive integers k and m with k ⩽ m there exists a separable metrizable space X ( k , m ) such that cmp X ( k , m ) = k and def X ( k , m ) = m . This solves Problem 6 from [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993, p. 71].