What happens when one light bulb in a series circuit burns out? a. nothing will happen. b. the rest of the bulbs continue to work. c. it breaks the circuit. d. the rest of the bulbs become dim?

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