Every closed orientable 3-manifold is a 3-fold branched covering space of $S^3$

Let p: M—>N be a nondegenerate simplicial map between compact triangulated manifolds of the same dimension n. This is a branched covering space if the restriction of p, called p*, gives a covering space map p>'. M(n 2 skeleton) —> N (n 2 skeleton). The set of points x in M such that p does not map any neighborhood of x homeomorphically into N is called the branch cover B. The (n 2)-dimensional set p(B) is called the branch set. J. W. Alexander asserted the following theorem [1] .