Bing-Whitehead Cantor sets were introduced by DeGryse and Osborne in dimension three and greater to produce examples of Cantor sets that were non standard (wild), but still had simply connected complement. In contrast to an earlier example of Kirkor, the construction techniques could be generalized to dimensions bigger than three. These Cantor sets in S are constructed by using Bing or Whitehea...

Assume G.C.H. and κ is the first uncountable cardinal such that there is a non-free κ-free abelian Whitehead group of cardinality κ. We prove that if all κ-free Abelian group of cardinality κ are Whitehead then κ is necessarily an inaccessible cardinal.