G-BASES IN FREE (LOCALLY CONVEX) TOPOLOGICAL VECTOR SPACES

Taras Banakh, Arkady Leiderman

Research output: Working paper/PreprintPreprint

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Abstract

We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\mathfrak G$-base. A topological space $X$ has a local $\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_\alpha)_{\alpha\in\omega^\omega}$ such that $U_\beta\subset U_\alpha$ for all $\alpha\le\beta$ in $\omega^\omega$. To construct $\mathfrak G$-bases in free topological vector spaces, we exploit a new description of the topology of a free topological vector space over a topological (or more generally, uniform) space.
Original languageEnglish GB
PublisherarXiv:1606.01967 [math.GN]
StatePublished - 2016

Keywords

  • math.GN
  • math.FA
  • math.LO
  • 54D70, 54D45, 46A03, 06A06, 54A35, 54C30, 54E15, 54E20, 54E35

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