Li, Xiujun; Dong, Yunbai; He, Hua A note on existence of nontrivial continuous linear functional on TVS. (English) Zbl 1093.46500 J. Hebei Univ. Technol. 34, No. 3, 62-64 (2005). Summary: We give a sufficient and necessary condition for the existence of non-trivial continuous linear functionals on topological vector spaces, and show that there is no nontrivial continuous linear functional on any quasi-bounded topological vector space. MSC: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) Keywords:quasi-bounded space; topological vector spaces PDFBibTeX XMLCite \textit{X. Li} et al., J. Hebei Univ. Technol. 34, No. 3, 62--64 (2005; Zbl 1093.46500)