  For a signature L with at least one constant symbol, an L-structure is called
minimal if it has no proper substructures. Let S_L be the set of isomorphism
types of minimal L-structures. The elements of S_L can be identified with
ultrafilters of the Boolean algebra of quantifier-free L-sentences, and
therefore one can define a Stone topology on S_L. This topology on S_L
generalizes the topology of the space of n-marked groups. We introduce a
natural ultrametric on S_L, and show that the Stone topology on S_L coincide
with the topology of the ultrametric space S_L iff the ultrametric space S_L is
compact iff L is locally finite (that is, L contains finitely many n-ary
symbols for any n). As one of the applications of compactness of the Stone
topology on S_L, we prove compactness of certain classes of metric spaces in
the Gromov-Hausdorff topology. This slightly refines the known result based on
Gromov's ideas that any uniformly totally bounded class of compact metric
spases is precompact.
