Alexandroff plank

Alexandroff plank in topology, an area of mathematics, is a topological space that serves as an instructive example.
Definition.
The construction of the Alexandroff plank starts by defining the topological space formula_1 to be the Cartesian product of formula_2 and formula_3, where formula_4 is the first uncountable ordinal, and both carry the interval topology. The topology formula_5 is extended to a topology formula_6 by adding the sets of the form
where formula_8.
The Alexandroff plank is the topological space formula_9.
It is called plank for being constructed from a subspace of the product of two spaces.
Properties.
The space formula_9 satisfies that: