$\mathfrak G$-bases in free (locally convex) topological vector spaces

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 $(U_α)_{α\inω^ω}$ such that $U_β\subset U_α$ for all $α\leβ$ in $ω^ω$. 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.

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