Differentiable open maps of (<i>p</i>+ 1)-manifold to<i>p</i>-manifold

Abstract

Let /: M*> +1 ->NP be a C 3 open map with p^l, let Rp-(f) be the critical set of /, and let for each y e N p Then (1.1) there is a closed set X<zM p+1 such that dim/(X) ^ p -2 and, for every xeM p+1 -X, there is a natural number d(x) with / at x locally topologically equivalent to the map