A subspace of R3 for which Cmp ≠ def

We construct a separable metric space E in R3 for which both the small and large compactness degrees cmp E=Cmp E=1 and the compactness deficiency def E=2. This improves on the example in R4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.