A construction of a fuzzy topology from a strong fuzzy metric (Q2825443)

A strong fuzzy metric is a fuzzy metric \(m\) for which \(m(x,z,t) \geq m(x,y,t)\star m(y,z,t)\) for all \(x,y,z \in X\) and \(t>0\) and it is continuous and non-decreasing in the third variable for all \(x,y \in X\). For complete sublattices \(L,M\) of the unit interval containing 0 and 1 the mapping \(\tau: L^X \to M\) is an \(LM\)-topology if it maps the constant functions 0 and 1 to 1, and for all sets in \(L^X\) there is \(\tau (A \land B) \geq \tau (A) \land \tau(B), \tau(\lor _i A_i) \geq \land _i \tau (A_i)\). An \(LM\)-topology induced by a strong fuzzy metric is constructed. Continuity on such topological spaces is studied.