Under OCA and MA_ℵ1(σ-linked), every coordinate respecting function between reduced products of separable metric spaces with uniformly bounded diameter is trivial.
Farah, Analytic quotients: theory of liftings for quotients over analytic ideals on the integers, Mem
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A metric lifting theorem
Under OCA and MA_ℵ1(σ-linked), every coordinate respecting function between reduced products of separable metric spaces with uniformly bounded diameter is trivial.