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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).
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What are the LCA groups that are the Pontryagin dual of a locally profinite abelian group?
For certain subcategories of LCA groups, we have nice descriptions of the dual category under Pontryagin duality (all groups are implicitly assumed to be abelian):
finite groups $\leftrightarrow$ fini …