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
- Full Text: false
- Reviewed:
- 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
Subspaces of the free topological vector space on the unit interval
- Authors: Gabriyelyan, Saak , Morris, Sidney
- Date: 2018
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 97, no. 1 (2018), p. 110-118
- Full Text: false
- Reviewed:
- Description: For a Tychonoff space X, let V(X) be the free topological vector space over X, A(X) the free abelian topological group over X and I the unit interval with its usual topology. It is proved here that if X is a subspace of I, then the following are equivalent: V(X) can be embedded in V(I) as a topological vector subspace; A(X) can be embedded in A(I) as a topological subgroup; X is locally compact. © 2017 Australian Mathematical Publishing Association Inc..