Local convexity and local boundedness of induced $I(L)$-topological vector spaces

Abstract

In this paper, we prove that an L-topological vector space is locally convex (locally bounded) iff its induced $I(L)$-topological vector space is locally convex (locally bounded), where $I(L)$ is the L-fuzzy unit interval. Also, we give a necessary and sufficient condition for the induced $I(L)$-topological vector space to be $I(L)$-fuzzy normable.