For L a closed sets lattice, we prove the existence and a characterization theorem of the minimal elements of T 3LX, where T 3

This paper studies local strong F1 connectedness and local Q-connectedness of L-topological spaces. It is shown that every L-interval J (L) and its weak induci.cation J(L) are both local strong F1 connected andlocal Q-connected, and that the local Q-connectedness of an L-topological space is equivalent to that of its induced I (L)-topological space.

Based on the consideration to the layer structures of fuzzy lattices and the level topologies of L-fuzzy topological spaces, a connectedness is dened for an arbitrary L-fuzzy set in this paper. This denition reects the degree of connectivity of an L-fuzzy set. It is shown that the connectedness of L-fuzzy topological spaces is an L-good extension, multiplicative and preserved under continuous L-valued Zadeh functions, and that the inverse limit of continuums is a continuum. General L-fuzzy intervals and H-intervals are dened and connectedness of them are proved. It is also shown that the connectedness of an L-fuzzy topological space is equivalent to the connectedness of its induced I (L)-fuzzy topological space.

Using the notion of remote neighborhood, we dene the separation axioms T0 and T1 in L-fuzzy topological spaces (L-fts). The relations between our denitions, Hutton and Reilly's, and Wang's are discussed, and the separations of Hutton's fuzzy unit interval and Gantner's fuzzy real line are examined. Characterizations of these L-fts are proved and a series of properties of them are investigated. Moreover, some results on minimal T0 L-fts and T1 L-fts are established, which will be used immediately in our subsequent discussion.

This paper is a sequel to Li (1999). For some classes F of L-valued Zadeh functions, we will discuss two problems connected with inverse limits in LTop, K1HLTop and K2HLTop: (1) Will the condition that all L-valued Zadeh functions between factor L-fts of two given inverse systems are in F imply that the induced limit LTop-morphism is in F? (2) Will the condition that all bonding L-valued Zadeh functions are in F imply that all projective L-valued Zadeh functions are in F?