Tychonoff plank

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 formula_1 and formula_2, where formula_3 is the first infinite ordinal and formula_4 the first uncountable ordinal. The deleted Tychonoff plank is obtained by deleting the point formula_5.
Properties.
The Tychonoff plank is a compact Hausdorff space and is therefore a normal space. However, the deleted Tychonoff plank is non-normal. Therefore the Tychonoff plank is not completely normal. This shows that a subspace of a normal space need not be normal. The Tychonoff plank is not perfectly normal because it is not a Gδ space: the singleton formula_6 is closed but not a Gδ set.
The Stone–Čech compactification of the deleted Tychonoff plank is the Tychonoff plank.