C^infinity function c-to-1

From: G. A. Edgar (edgar_at_math.ohio-state.edu)
Date: 02/14/05 

Date: 14 Feb 05 08:13:44 -0500 (EST)

A colleague asked for a reference for:

There exists a C infinity function from R into R such that the inverse
image
of every real number is uncountable.