An
L
,
M
-fuzzy topological convergence structure on a set
X
is a mapping which defines a degree in
M
for any
L
-filter (of crisp degree) on
X
to be convergent to a molecule in
L
X
. By means of
L
,
M
-fuzzy topological neighborhood operators, we show that the category of
L
,
M
-fuzzy topological convergence spaces is isomorphic to the category of
L
,
M
-fuzzy topological spaces. Moreover, two characterizations of
L
-topological spaces are presented and the relationship with other convergence spaces is concretely constructed.
Local T_3 Constant Filter Convergence Spaces
