Metric topology on the L-fuzzy real line

In this paper, four gauge functionals on L-fuzzy real line R(L) are introduced and a pointwise pseudo-metric function on R(L) is given by means of them. It is pointed out that this metric function is identical with the Erceg metric function, and the metric topology is identical with the usual topology. Some relations between the families of neighborhood balls and remote-neighborhood balls are revealed.