On Free Locally Convex Spaces

Taras Banakh, Saak Gabriyelyan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let L(X) be the free locally convex space over a Tychonoff space X. We prove that the following assertions are equivalent: (i) every functionally bounded subset of X is finite, (ii) L(X) is semi-reflexive, (iii) L(X) has the Grothendieck property, (iv) L(X) is semi-Montel. We characterize those spaces X, for which L(X) is c0-quasibarrelled, distinguished or a (d f)-space. If X is a convergent sequence, then L(X) has the Glicksberg property, but the space L(X) endowed with its Mackey topology does not have the Schur property.

Original languageEnglish
Pages (from-to)6393-6401
Number of pages9
Issue number18
StatePublished - 1 Jan 2022


  • (d f)-space
  • Grothendieck property
  • b-feral
  • c-quasibarrelled
  • free locally convex space

ASJC Scopus subject areas

  • General Mathematics


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