- Title
- A topological group observation on the Banach-Mazur separable quotient problem
- Creator
- Gabriyelyan, Saak; Morris, Sidney
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/169235
- Identifier
- vital:13972
- Identifier
-
https://doi.org/10.1016/j.topol.2019.02.036
- Identifier
- ISBN:0166-8641
- Abstract
- The Separable Quotient Problem of Banach and Mazur asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space. It has remained unsolved for 85 years but has been answered in the affirmative for special cases such as reflexive Banach spaces. An affirmative answer to the Separable Quotient Problem would obviously imply that every infinite-dimensional Banach space has a quotient topological group which is separable, metrizable, and infinite-dimensional in the sense of topology. In this paper it is proved that every infinite-dimensional Banach space has as a quotient group the separable metrizable infinite-dimensional topological group, T
- Publisher
- Elsevier
- Relation
- Topology and Its Applications Vol. 259, no. (2019), p. 283-286
- Rights
- Copyright © 2019 Elsevier B.V. All rights reserved.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0199 Other Mathematical Sciences; Banach space; Frechet space; Quotient space; Separable; Topological group; Quotient group; Locally convex space; Circle group; Separable Quotient Problem
- Full Text
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