## Taiwanese Journal of Mathematics

### ON CLOSEDNESS IN THE $\mathcal{L}$-TOPOLOGY OF T.V.S.

#### Abstract

Let $X$ and $Y$ be Hausdorff and locally convex topological vector spaces. In this paper, we prove that a convex subset of $X$ is closed if and only if it is closed in the topology on $X$ induced by the set of continuous linear mappings from $X$ into $Y$ . As applications, some existence results for vector equilibrium problems and vector variational inequalities associated with discontinuous mappings are given.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 1 (2006), 129-138.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403804

Digital Object Identifier
doi:10.11650/twjm/1500403804

Mathematical Reviews number (MathSciNet)
MR2186167

Zentralblatt MATH identifier
1110.49017

#### Citation

Chiang, Y.; Wang, Y. S. ON CLOSEDNESS IN THE $\mathcal{L}$-TOPOLOGY OF T.V.S. Taiwanese J. Math. 10 (2006), no. 1, 129--138. doi:10.11650/twjm/1500403804. https://projecteuclid.org/euclid.twjm/1500403804