We know that metric spaces are normal. We also know that a uniform space is Hausdorff if the intersection of all entourages is the diagonal, in which case it is even regular.
However, is there a necessary and sufficient criterion to ensure that a uniform space is normal (A sufficient condition would be, for example, the space is metrizable)? I have read Bourbaki, General Topology as well as Willard, General topology, but I was not able to find any.
Thanks in advance.