Identify the best support for a separatory funnel. Select one: Tripod stand Three-prong clamp on a ring stand Iron ring clamped to a ring stand Iron ring with wire gauze

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k