Vol. 42, No. 3, 1972

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Topologies on structure spaces of lattice groups

S. J. Bernau

Vol. 42 (1972), No. 3, 557–568

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.

Mathematical Subject Classification 2000
Primary: 06A55
Secondary: 54G10
Received: 11 June 1971
Revised: 13 October 1971
Published: 1 September 1972
S. J. Bernau