Your teacher burns a piece of steel wool in class, demonstrating the chemical property, flammability. You are curious to see what other things can demonstrate chemical properties. Which of these does not demonstrate a chemical change?

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