Vol. 50, No. 1, 1974

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Real analytic open maps

Philip Throop Church and James Timourian

Vol. 50 (1974), No. 1, 37–42
Abstract

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

ϕd(x) : C × Rp−1 → R × Rp−1

defined by ϕd(x)(z,t1,,tp1) = ((zd(x)),t1,,tp1).

Mathematical Subject Classification 2000
Primary: 57D35
Secondary: 32C05
Milestones
Received: 21 August 1972
Published: 1 January 1974
Authors
Philip Throop Church
James Timourian