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The Tubby Torus as a Quotient Group
School of Science, Engineering and Information Technology, Federation University Australia, P.O.B. 663, Ballarat, VIC 3353, Australia
Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC 3086, Australia
Axioms 2020, 9(1), 11; https://doi.org/10.3390/axioms9010011
Received: 23 December 2019 / Revised: 14 January 2020 / Accepted: 17 January 2020 / Published: 20 January 2020
(This article belongs to the Collection Topological Groups)
Let E be any metrizable nuclear locally convex space and
the Pontryagin dual group of E. Then the topological group has the tubby torus (that is, the countably infinite product of copies of the circle group) as a quotient group if and only if E does not have the weak topology. This extends results in the literature related to the Banach–Mazur separable quotient problem.
Keywords: torus; tubby torus; separable quotient problem; locally convex space; nuclear space; Banach space; pontryagin duality; weak topology
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Morris, S.A. The Tubby Torus as a Quotient Group. Axioms 2020, 9, 11.
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Morris SA. The Tubby Torus as a Quotient Group. Axioms. 2020; 9(1):11.Chicago/Turabian Style
Morris, Sidney A. 2020. "The Tubby Torus as a Quotient Group." Axioms 9, no. 1: 11.
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