  We give a prescription to add the gravitational field of a global topological
defect to a solution of Einstein's equations in an arbitrary number of
dimensions. We only demand that the original solution has a O(n) invariance
with n greater or equal 3. We will see that the general effect of a global
defect is to introduce a deficit solid angle. We also show how the same kind of
scalar field configurations can be used for spontaneous compactification of "n"
extra dimensions on an n-sphere.
