In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures. It is defined as the topological product of the two ordinal spaces [ 0 , ω 1 ] {\displaystyle [0,\omega _{1}]} and [ 0 , ω ] {\displaystyle [0,\omega ]} , where ω {\displaystyle \omega } is the first infinite ordinal and ω 1 {\displaystyle \omega _{1}} the first uncountable ordinal.
In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures. It is defined as the topological product of the two ordinal spaces [ 0 , ω 1 ] {\displaystyle [0,\omega _{1}]} and [ 0 , ω ] {\displaystyle [0,\omega ]} , where ω {\displaystyle \omega } is the first infinite ordinal and ω 1 {\displaystyle \omega _{1}} the first uncountable ordinal.
Source: Wikipedia "Tychonoff plank" · CC BY-SA 4.0
Share this article: X · Bluesky