In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures.
It is defined as the topological product of the two ordinal spaces
The Tychonoff plank is a compact Hausdorff space and is therefore a normal space.
However, the deleted Tychonoff plank is non-normal.
[1] Therefore the Tychonoff plank is not completely normal.
The Tychonoff plank is not perfectly normal because it is not a Gδ space: the singleton
is closed but not a Gδ set.