Embeddings of free topological vector spaces

Arkady Leiderman, Sidney A. Morris

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)311-324
Number of pages14
JournalBulletin of the Australian Mathematical Society
Volume101
Issue number2
DOIs
StatePublished - 1 Apr 2020

Keywords

  • Cook continuum
  • embedding
  • free locally convex space
  • free topological vector space
  • rigid Bernstein set
  • variety of locally convex spaces

ASJC Scopus subject areas

  • Mathematics (all)

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