Maps with 0-dimensional critical set

Let /: M n -> N* be O with np = 0 or 1, let p ^ 2, and let Rp-tif) be the critical set of /. If dim (R p ^ (f) ) S 0, then (1. 1) at each x 6 M n, f is locally topologically equivalent to one of the following maps: (a) the projection map p: R n - R p, (b): C->C defined by (z) = z d (d = 2, 3, ), where C is the complex plane, or (c) r: C X C->CxR defined by (z, w) = (2 w, M 2 -|z| 2), where w is the complex conjugate of w.