Induced I( L)-fuzzy topological vector spaces

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In this paper we introduce and study the induced I( L)-fuzzy topological vector spaces. The following main result is proved: If ( L X , δ) is an L-fuzzy topological vector space, then ( I( L) X , ω I( L) ( δ)) is an I( L)-fuzzy topological vector space, where I( L) is the fuzzy unit interval and ω I( L) ( δ) is the induced I( L)-fuzzy topology of the L-fuzzy topology δ. Furthermore, we also prove that the induced I( L)-fuzzy topological vector spaces ( I( L) X , ω I( L) ( δ)) preserve the product and quotient space as well.