quotient. Property (i) is immediate from (a). For property (ii), suppose U ⊂XS is open and invariant. Then Z= X−U is closed and invariant, so ϕ(Z) is closed in Y. Let V = YS −ϕ(Z). Then ϕ|−1 XS (V) ⊂U, but if x∈U, then O(x) is closed and invariant, in XS, and Z∩O(x) = …