\begin{definition}[Definition:Alexandroff Plank]
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Let $\Omega$ be the first uncountable ordinal.
Let the closed ordinal space $\closedint 0 \Omega$ be given the interval topology.
Let the closed real interval $\closedint {-1} 1$ be given the interval topology.
Let $\struct {S, \tau}$ be the product space of $\closedint 0 \Omega$ with $\closedint {-1} 1$
Consider the point $p := \tuple {\Omega, 0} \in S$
Let $\sigma$ be the expansion of $\tau$ generated by adding to $\tau$ the sets of the form:
:$\map U {\alpha, n} := \set p \cup \hointl \alpha \Omega \times \openint 0 {\dfrac 1 n}$
Then the topological space $T = \struct {S, \sigma}$ is known as the '''Alexandroff plank'''.
\end{definition}