A hereditarily normal square
A. Ostaszewski used \(\diamondsuit\) to construct a countably compact perfectly normal noncompact space. The author modifies this construction to obtain a space which, in addition, has a hereditarily normal square. Since countably compact spaces with a hereditarily normal square are perfectly normal, it follows that the existence of countably compact noncompact spaces with a hereditarily normal square is independent of the axioms of ZFC.
scientific article; zbMATH DE number 527419