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Open AccessArticle

The Tubby Torus as a Quotient Group

1
School of Science, Engineering and Information Technology, Federation University Australia, P.O.B. 663, Ballarat, VIC 3353, Australia
2
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 E ^ the Pontryagin dual group of E. Then the topological group E ^ 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. View Full-Text
Keywords: torus; tubby torus; separable quotient problem; locally convex space; nuclear space; Banach space; pontryagin duality; weak topology torus; tubby torus; separable quotient problem; locally convex space; nuclear space; Banach space; pontryagin duality; weak topology
MDPI and ACS Style

Morris, S.A. The Tubby Torus as a Quotient Group. Axioms 2020, 9, 11.

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