## Collapse a closed subset of a uniform space.

I have proved that if you collapse a closed subset of a separated (Hausdorff) uniform space to a point, you get a separated uniform space. Surely such a simple result must be standard, but I can't find anything about that in Isbell's book, which is the only reference I have for uniformities. Can someone supply a reference. Note that the corresponding fact for topological spaces fails.

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