- Title
- Free subspaces of free locally convex spaces
- Creator
- Gabriyelyan, Saak; Morris, Sidney
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/165181
- Identifier
- vital:13218
- Identifier
-
https://doi.org/10.1155/2018/2924863
- Identifier
- ISBN:2314-8896
- Abstract
- Abstract If X and Y are Tychonoff spaces, let and be the free locally convex space over and , respectively. For general and , the question of whether can be embedded as a topological vector subspace of is difficult. The best results in the literature are that if can be embedded as a topological vector subspace of , where , then is a countable-dimensional compact metrizable space. Further, if is a finite-dimensional compact metrizable space, then can be embedded as a topological vector subspace of . In this paper, it is proved that can be embedded in as a topological vector subspace if is a disjoint union of a countable number of finite-dimensional locally compact separable metrizable spaces. This is the case if It is also shown that if and denote the Cantor space and the Hilbert cube , respectively, then (i) is embedded in if and only if is a zero-dimensional metrizable compact space; (ii) is embedded in if and only if is a metrizable compact space.
- Publisher
- Hindawi Limited
- Relation
- Journal of Function Spaces Vol. 2018, no. (2018), p. 1-5
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2018 Saak S. Gabriyelyan and Sidney A. Morris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Topological vector-spaces; Unit interval; Mathematics
- Full Text
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