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

2016/06/06 by Banakh, Taras, Leiderman, Arkady
#06A06 #46A03 #54A35 #54C30 #54D45 #54D70 #54E15 #54E20 #54E35 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1606.01967

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_α)_α∈ω^ω such that U_β⊂ U_α for all α≤β 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.

Related

• Free locally convex spaces with a small base
• A description of the topology of free topological vector spaces
• The characterizations of hyperspaces and free topological groups with an ω^ω-base
• Free topological vector spaces
• ω^ω-Base and infinite-dimensional compact sets in locally convex spaces