Some problems of regularity of f-quasimetrics

We get a new proof for validity of T₄-axiom of separation for weak symmetric f-quasimetric spaces. Using this proof we get T₄- property for more general classes of f-quasimetric spaces. We construct the symmetric (q,q)-quasimetric space (X,d) such that distance function d(u,v) is continuous to each variables but (ρ(x₀,x_n) + ρ(y₀; y_n)) 0 ρ(x_n,y_n) = ρ(x₀,y₀).