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