On compactness of induced I( L)-fuzzy topological spaces

Abstract

The induced I( L)-fuzzy topological spaces for L-fuzzy topological spaces introduced by Wang Geping is a kind of important fuzzy topological space. In this paper, the author studies the fuzzy compactness of induced I( L)-fuzzy topological spaces. Some available relations between molecular nets of an L-fuzzy topological space and that of its induced I( L)-fuzzy topological space are firstly presented. By using these relations, the author obtains that the induced I( L)-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact) if and only if the L-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact). The author also proves that the induced I( L)-fuzzy topological space is ∗-paracompact if and only if the L-fuzzy topological space is ∗-paracompact.