Based on the notions of fuzzy connectedness defined by Lu and Li [Fuzzy connectedness: new definitions and comparisons, Fuzzy Sets and Systems 157(2006)1928–1940], some new fuzzy local connectedness, such as local connectedness, local ultra-
F1 connectedness, local strong
F1 connectedness, local ultra-
F2 connectedness, local strong
F2 connectedness, ultra-
F1 local connectedness, strong
F1 local connectedness, ultra-
F2 local connectedness, and strong
F2 local connectedness, of
L-topological spaces or
L-cotopological spaces are defined in this paper. Apart from maintaining some frequently used properties that classical local connected topological spaces possess,
L-topological spaces or
L-cotopological spaces which satisfy our new fuzzy local connectedness axioms also have some interesting properties. For example, local connectedness, local ultra-
F1 connectedness, local ultra-
F2 connectedness, local strong
F1 connectedness, and local strong
17a5c6fbe27cf5d"" title=""Click to view the MathML source"">F2 connectedness are all
I(L)-inducible if
L is a complete and meet-continuous deMorgan algebra; they are
L-extension of local connectedness of topological spaces under some moderate restrictions to
7a023790b3f952110abb57b76c"" title=""Click to view the MathML source"">L. It is proved that all
7a0ca20263803b522c8dccaf200941"" title=""Click to view the MathML source"">L-intervals are locally connected if
Copr(L) is a
a059a34"" title=""Click to view the MathML source"">![]()
-generating set of
L. Some categorical results reflecting the differences between classical topology and
L-topology are obtained, the relationships between these notions of connectedness are also investigated in detail.
