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The Tubby Torus as a Quotient Group
- Source :
- Axioms, Vol 9, Iss 1, p 11 (2020)
- Publication Year :
- 2020
- Publisher :
- MDPI AG, 2020.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 9
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Axioms
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.01a5c548e143a19537b7dc9218ff7a
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/axioms9010011