A structure space of a lattice
group G is, coventionally, a set of prime subgroups of G with the hull-kernel topology.
The set of all prime subgroups of G, together with G when G has no strong unit,
carries a natural topology, stronger than the hull-kernel topology, which is compact
and Hausdorff. There is a natural closed subspace which is a quotient of the Stone
space of the complete Boolean algebra of polar subgroups. Under the hull-kernel
topology this subspace is a retract of the space of prime subgroups, but no
longer closed. These topologies are compared, with particular reference to
coincidences.
