Real analytic open maps

Philip Throop Church and James Timourian

Vol. 50 (1974), No. 1, 37–42

DOI: 10.2140/pjm.1974.50.37

Abstract

Let R and C be the real and complex fields, respectively, and for ζ ∈ C let ℛ(ζ) be the real part of ζ. If f : M^p+1 → N^p is real analytic and open with p ≧ 1, then there is a closed subspace X ⊂ M^p+1 such that dimf(X) ≦ p − 2 and, for every x ∈ M^p+1 − X, there is a natural number d(x) with f at x locally topologically equivalent to the map

defined by ϕ_d(x)(z,t₁,⋯,t_p−1) = (ℛ(z^d(x)),t₁,⋯,t_p−1).

Mathematical Subject Classification 2000

Primary: 57D35

Secondary: 32C05

Milestones

Received: 21 August 1972

Published: 1 January 1974