Tychonoff plank

In

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

Properties

The Tychonoff plank is a

: the singleton ${\displaystyle \{\infty \}}$ is closed but not a G_δ set.

The Stone–Čech compactification of the deleted Tychonoff plank is the Tychonoff plank.^[2]

Notes

See also

• List of topologies

References

• MR 0370454
• MR 0507446
• Willard, Stephen (1970), General Topology,
  MR 0264581