Free locally convex spaces and the k-space property

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10 Scopus citations

Abstract

Let L(X) be the free locally convex space over a Tychonoff space X. Then L(X) is a k-space if and only if X is a countable discrete space. We prove also that L(D) has uncountable tightness for every uncountable discrete space D.

Original languageEnglish
Pages (from-to)803-809
Number of pages7
JournalCanadian Mathematical Bulletin
Volume57
Issue number4
DOIs
StatePublished - 1 Dec 2014

Keywords

  • Countable tightness
  • Free locally convex space
  • K-space

ASJC Scopus subject areas

  • Mathematics (all)

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