Chromatic Number of the Plane Meets Map Coloring: Townsend–Woodall’s 5-Color Theorem

In Chapter 8 , I described Douglas R. Woodall’s 1973 attempt to obtain a result on chromatic number of the plane under an additional condition that monochromatic sets are closed or simultaneously divisible into regions [Woo1]. Six years after his publication, Stephen P. Townsend found a logical mistake in Woodall’s proof, constructed a counterexample showing that Woodall’s proof cannot work and went on to discover his own proof of the following major result.