Thus G is an abelian group with a topology making the group operations continuous functions from G and G 2 to G , and under which any point has a neighborhood contained in a compact set.
Q p are also lcag's for each prime p .
An example of a topological abelian group that is not locally compact is an infinite-dimensional Hilbert space. Except for that last sentence, the properties of Pontrjagin duality may remind you of duality of vector spaces.