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Jan 12, 2016 at 7:28 comment added Henno Brandsma The OP asked about $\mathcal{D}_F$ (defined in terms of the topology on $X \times X$). Is the uniformity generated by $\mathcal{D}_F$ the same as the one generated by your $\mathcal{B}$?
Jan 5, 2016 at 14:28 history answered Dominic van der Zypen CC BY-SA 3.0