  It is well known that the lattice Idc G of all principal {\ell}-ideals of any
Abelian {\ell}-group G is a completely normal distributive 0-lattice, and that
not every completely normal distributive 0-lattice is a homomorphic image of
some Idc G, via a counterexample of cardinality $\aleph 2. We prove that every
completely normal distributive 0-lattice with at most $\aleph 1 elements is a
homomorphic image of some Idc G. By Stone duality, this means that every
completely normal generalized spectral space, with at most $\aleph 1 compact
open sets, is homeomorphic to a spectral subspace of the {\ell}-spectrum of
some Abelian {\ell}-group.
