Embeddings of free topological vector spaces

Title: Embeddings of free topological vector spaces
Creator: Leiderman, Arkady; Morris, Sidney
Date: 2020
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/171983
Identifier: vital:14436
Identifier: https://doi.org/10.1017/S000497271900090X
Identifier: ISBN:0004-9727 (ISSN)
Abstract: It is proved that the free topological vector space contains an isomorphic copy of the free topological vector space for every finite-dimensional cube , thereby answering an open question in the literature. We show that this result cannot be extended from the closed unit interval to general metrisable spaces. Indeed, we prove that the free topological vector space does not even have a vector subspace isomorphic as a topological vector space to , where is a Cook continuum, which is a one-dimensional compact metric space. This is also shown to be the case for a rigid Bernstein set, which is a zero-dimensional subspace of the real line. © 2019 Australian Mathematical Publishing Association Inc..
Publisher: Cambridge University Press
Relation: Bulletin of the Australian Mathematical Society Vol. 101, no. 2 (2020), p. 311-324
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Cook continuum; embedding; free locally convex space; free topological vector space; rigid Bernstein set; variety of locally convex spaces
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