Definition:Tychonoff Plank/Deleted

Definition
Let $T = \struct {S, \tau}$ denote the Tychonoff plank.

Let $\omega$ be the first transfinite ordinal.

Let $\Omega$ be the first uncountable ordinal.

Let $S = \closedint 0 \omega$ and $\closedint 0 \Omega$ be closed ordinal spaces which have both been given the interval topology.

Hence let $T = \struct {S, \tau}$ denote the Tychonoff plank.

The deleted Tychonoff plank is the topological subspace defined as:
 * $T_\infty = \struct {S \setminus \set {\tuple {\Omega, \omega} }, \tau}$

Also see

 * Deleted Tychonoff Plank is Topology