The Connectedness Relative to a Sub-base in the L-Fuzzy Topological Space

The upper approximation set and the lower approximation set, which are the two most important concepts in the theory of covering generalized rough sets can be respectively represented by the relative interior and relative closure relative to sub-base in the L-fuzzy topological space. On the other hand, in general topology, there are different ways to describe connectivity of a subset, may be the K. Fan´s theorem is the most interesting one. In this paper, we shall define the concept of connectedness relative to sub base of the L-fuzzy topology in this way. Such connectedness is weaker than that of the L-fuzzy topology, but hey share many similar properties. These properties are in fact the generalization of the connectedness.