Embedding into free topological vector spaces on compact metrizable spaces
- Authors: Gabriyelyan, Saak , Morris, Sidney
- Date: 2018
- Type: Text , Journal article
- Relation: Topology and its Applications Vol. 233, no. (2018), p. 33-43
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- Description: For a Tychonoff space X, let V(X) be the free topological vector space over X. Denote by I, G, Q and Sk the closed unit interval, the Cantor space, the Hilbert cube Q=IN and the k-dimensional unit sphere for k
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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- Reviewed:
- 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