Topology of a separated uniformity

Reference no: EM13966712

A uniform space (S, U ) is called separated iff for every x /= y in S, there is a U ∈ U with (x, y) ∈/ U .

(a) Show that the uniform topology of a separated uniformity is always Hausdorff.

(b) Show that if S has more than one point, a separated uniformity never converges as a filter for its product topology.

Reference no: EM13966712

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