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 $[0,\omega ]$ $[0,\omega ]$ and $[0,\omega _{1}]$ $[0,\omega_1]$ , where $\omega$ $\omega$ is the first infinite ordinal and $\omega _{1}$ $\omega _{1}$ the first uncountable ordinal. The deleted Tychonoff plank is obtained by deleting the point $\infty =(\omega ,\omega _{1})$ $\infty =(\omega ,\omega _{1})$ .