The role of the diagonal operator in fuzzy topology (Q1111187)

The authors introduce fuzzy closure and topological fuzzy closure in the usual manner. Previously they studied characterizing properties for fuzzy topological convergence and observed that the idempotency of closure is not relevant for looking at the definition of convergence and its elementary properties. The same definition of convergence can be formulatd starting with a non-idempotent closure. The authors formulate fuzzy versions of `diagonal condition' and `weak diagonal condition' and use them to show the exact role of the idempotency of closure with regard to convergence.