Simple Abelian topological groups

Dominic Bush-Hipwood

Frank Adams 1,

An abelian topological group G is topologically simple if it's only closed subgroups are {0} and G. In 1976 a mathematician called R.C.Hooper asked the question (which remains open): Does there exist an infinite abelian group that is metrizable, complete and topologically simple? We will explore this question and give an example when we drop the need for completeness.  

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