Abstract
The aim of the paper is mainly to introduce and study I type of strong connectivity in L-fuzzy topological space. It preserves many good properties of connected sets in general topological spaces: The sets between I type of strongly connected set and its semiclosure are I type of strongly connected. Any union of I type of strongly connected sets with non-null intersection is I type of strongly connected. The images of irresolute order-homomorphisms of I type of strongly connected sets are I type of strongly connected. For I type of strong connectivity the K. Fan's Theorem holds.
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