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A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric $d_X$ of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set $d_X(a,b):a,b\in A$ does not exceed the density of A, $|d_X\left(A\times A\right)|\le dens\left(A\right)$. The construction of the space X determines a functor : Top...