A topological group observation on the Banach-Mazur separable quotient problem
- Authors: Gabriyelyan, Saak , Morris, Sidney
- Date: 2019
- Type: Text , Journal article
- Relation: Topology and Its Applications Vol. 259, no. (2019), p. 283-286
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- Description: 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
An open mapping theorem
- Authors: Gabriyelyan, Saak , Morris, Sidney
- Date: 2016
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 94, no. 1 (2016), p. 65-69
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- Description: It is proved that any surjective morphism f : Z(k) -> K onto a locally compact group K is open for every cardinal k. This answers a question posed by Hofmann and the second author.