# Definition:Tychonoff Plank

## Definition

Let $\omega$ be the first transfinite ordinal.

Let $\Omega$ be the first uncountable ordinal.

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

The Tychonoff plank is the topological space defined as:

$T = \closedint 0 \Omega \times \closedint 0 \omega$

### Deleted Tychonoff Plank

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 Tychonoff plank can be found here.

## Source of Name

This entry was named for Andrey Nikolayevich Tychonoff.