The sun's apparent motion across the sky from east to west daily is due to the
a) rotation of the sun.
b) rotation of the earth.
c) orbit of the earth around the sun.
d) orbit of the sun around the earth.

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