\begin{definition}[Definition:Dieudonné Plank]
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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:
{{begin-eqn}}
{{eqn | l = \map {U_\alpha} \beta
      | r = \set {\tuple {\beta, \gamma}: \alpha < \gamma \le \omega}
}}
{{eqn | l = \map {V_\alpha} \beta
      | r = \set {\tuple {\gamma, \beta}: \alpha < \gamma \le \Omega}
}}
{{end-eqn}}
The topological space $\struct {S, \tau}$ is known as the '''Dieudonné plank'''.
\end{definition}