2017/06/07 by Fucai Lin, Lin, Fucai, Shou Lin +3
Computer Science · Mathematics · #22A05 #46A05 #54A25 #54D50 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1706.02190
openalex publication_date 2017/06/07 · openalex created_date 2017/06/15 · openalex updated_date 2026/07/28
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 map 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 and countable tightness of free topological vector space over some generalized metric spaces are studied. The characterization of a space X is given such that the free topological vector space V(X) is a k-space or the tightness of V(X) is countable. Furthermore, the characterization of a space X is also provided such that if the fourth level of V(X) has the k-property or is of the countable tightness then V(X) is too.