| Summary: | Let <i>E</i> be any metrizable nuclear locally convex space and <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>E</mi> <mo>^</mo> </mover> </semantics> </math> </inline-formula> the Pontryagin dual group of <i>E</i>. Then the topological group <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>E</mi> <mo>^</mo> </mover> </semantics> </math> </inline-formula> has the tubby torus (that is, the countably infinite product of copies of the circle group) as a quotient group if and only if <i>E</i> does not have the weak topology. This extends results in the literature related to the Banach−Mazur separable quotient problem.
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