# Definition:Tychonoff Plank/Deleted

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## 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

- Results about
**the deleted Tychonoff plank**can be found here.

## Source of Name

This entry was named for Andrey Nikolayevich Tychonoff.

## Sources

- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*(2nd ed.): Part $\text {II}$: Counterexamples: $87$. Deleted Tychonoff Plank