  We establish a topological duality for bounded lattices. The two main
features of our duality are that it generalizes Stone duality for bounded
distributive lattices, and that the morphisms on either side are not the
standard ones. A positive consequence of the choice of morphisms is that those
on the topological side are functional. Towards obtaining the topological
duality, we develop a universal construction which associates to an arbitrary
lattice two distributive lattice envelopes with a Galois connection between
them. This is a modification of a construction of the injective hull of a
semilattice by Bruns and Lakser, adjusting their concept of 'admissibility' to
the finitary case. Finally, we show that the dual spaces of the distributive
envelopes of a lattice coincide with completions of quasi-uniform spaces
naturally associated with the lattice, thus giving a precise spatial meaning to
the distributive envelopes.
