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 ${\displaystyle [0,\omega _{1}]}$ and ${\displaystyle [0,\omega ]}$, where ${\displaystyle \omega }$ is the first infinite ordinal and ${\displaystyle \omega _{1}}$ the first uncountable ordinal. The deleted Tychonoff plank is obtained by deleting the point ${\displaystyle \infty =(\omega _{1},\omega )}$.