Abstract
The free topological vector space V(X) over a Tychonoff space X is a pair consisting of a topological vector space V(X) and a continuous mapping i=iX:X→V(X) such that every continuous mapping f from X to a topological vector space E gives rise to a unique continuous linear operator f‾:V(X)→E with f=f‾∘i. In this paper, the k-property, Fréchet-Urysohn property, κ-Fréchet-Urysohn property and countable tightness of free topological vector space over some class of generalized metric spaces are studied. First, we mainly discuss the characterization of a space X such that V(X) or the third level of V(X) is Fréchet-Urysohn or κ-Fréchet-Urysohn, respectively. Then we give the characterization of a space X such that the second level of V(X) is of countable tightness or is a k-space, respectively.
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