- Title
- Subspaces of the free topological vector space on the unit interval
- Creator
- Gabriyelyan, Saak; Morris, Sidney
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/164219
- Identifier
- vital:12998
- Identifier
-
https://doi.org/10.1017/S0004972717000673
- Identifier
- ISBN:0004-9727
- Abstract
- 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..
- Publisher
- Cambridge University Press
- Relation
- Bulletin of the Australian Mathematical Society Vol. 97, no. 1 (2018), p. 110-118
- Rights
- Copyright © 2017 Australian Mathematical Publishing Association Inc.
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Embedding; Free abelian topological group; Free topological group; Free topological vector space; Locally compact
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