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  and , where  is the first infinite ordinal and  the first uncountable ordinal. The deleted Tychonoff plank is obtained by deleting the point . 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  is closed but not a Gδ set. The Stone–Čech compactification of the deleted Tychonoff plank is the Tychonoff plank. Notes

See also 

 List of topologies

References 
 
 
 

Topological spaces