Deep lexical acquisition of verb-particle constructions

Using the Pontryagin Duality and results of S. Fisher, P. Gartside (1991); P. Gartside, M. Smith (2007) and Y.D. Cornulier, L. Guyot, W. Pitsch (2008) we show that the space S(A) of all closed subgroups of a compact Abelian group A is countable if and only if there is a closed subgroup K of A such that K is topologically isomorphic to ⊕h i=1 Zpi⊕G and A/K is topologically isomorphic to T ⊕ G̃, where G, G̃ are finite abelian groups and all pi’s are distinct primes. And in this case S(A) is homeomorphic to S × [m], where n 6= m can be computed exactly. Here S is homeomorphic to the subset {1/n : n ≥ 1} ∪ {0} of R and [m] = {0, 1, . . . ,m− 1}.