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Some cases of preservation of the Pontryagin dual by taking dense subgroups. (English) Zbl 1235.22004
For an abelian topological group $G$ let $G^\wedge$ denote the group of continuous characters of $G$, endowed with the compact-open topology. A dense subgroup $H$ of an abelian topological group $G$ is said to {\it determine} $G$ if the restriction operator $G^\wedge\to H^\wedge$ is a topological isomorphism. An abelian topological group is {\it determined} if each dense subgroup of $G$ determines $G$. The authors detect some operations preserving determined groups and present several representative examples of determined and non-determined groups. One of the main results is Theorem 14 saying that each compact abelian group $G$ of weight $w(G)\ge \mathfrak c$ contains a dense pseudocompact subgroup which does not determine $G$.

22A05Structure of general topological groups
Full Text: DOI
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