Definition:Dieudonné Plank

Definition
Let $\omega$ be the first transfinite ordinal.

Let $\Omega$ be the first uncountable ordinal.

Let $S = \paren {\closedint 0 \omega \times \closedint 0 \Omega} \setminus \set {\tuple {\Omega, \omega} }$ be the underlying set of the deleted Tychonoff plank.

Let the topology $\tau$ be generated by declaring as open:


 * each point of $\hointr 0 \omega \times \hointr 0 \Omega$

together with the sets defined as:

The topological space $\struct {S, \tau}$ is known as the Dieudonné plank.

Also see

 * Dieudonné Plank is Topology