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Boolean algebra.[clarification needed] For any ordinal number λ one can consider the spaces of ordinal numbers [ 0 , λ ) = { α ∣ α < λ } {\displaystyle...

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...

compact, first-countable spaces that are not compact (these are necessarily not metrizable spaces). One such space is the ordinal space [ 0 , ω 1 ) . {\displaystyle...

In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance...

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are...

uncountable ordinal, traditionally denoted by ω 1 {\displaystyle \omega _{1}} or sometimes by Ω {\displaystyle \Omega } , is the smallest ordinal number that...

Hilbert space Fréchet space Hilbert cube Order topology Open ordinal space [0,Γ) where Γ<Ω Closed ordinal space [0,Γ] where Γ<Ω Open ordinal space [0,Ω)...

In topology, the Tychonoff plank is a topological space defined using ordinal spaces that is a counterexample to several plausible-sounding conjectures...

G_{\delta \sigma }.} to the first uncountable ordinal. To prove this claim, any open set in a metric space is the union of an increasing sequence of closed...

In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories...

best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement...

a compactly generated space are not compactly generated in general, even in the Hausdorff case. For example, the ordinal space ω 1 + 1 = [ 0 , ω 1 ] {\displaystyle...

Sword Art Online the Movie: Ordinal Scale (Japanese: 劇場版 ソードアート・オンライン -オーディナル・スケール-, Hepburn: Gekijō-ban Sōdo Āto Onrain -Ōdinaru Sukēru-) is a 2017 Japanese...

south, and west are at 90 degree intervals in the clockwise direction. The ordinal directions (also called the intercardinal directions) are northeast (NE)...

by ωω (not to be confused with the countable ordinal obtained by ordinal exponentiation). The Baire space is defined to be the Cartesian product of countably...

The number of the rank in question was indicated by ordinal numbers, in abbreviation with the ordinal indicator (a superscript o). Use of "degree" specifically...

"too long" (indexed by too large an ordinal) to compress into a sequence. Sequential spaces are those topological spaces for which nets of countable length...

to find the ordinal number of a particular object, or to find the object with a particular ordinal number, corresponds to assigning ordinal numbers one...

subsequence. If a space is a metric space, then it is sequentially compact if and only if it is compact. The first uncountable ordinal with the order topology...

{\Bigr \}},} where α {\displaystyle \alpha } is an ordinal and λ {\displaystyle \lambda } is a limit ordinal. The cardinal ℶ 0 = ℵ 0 {\displaystyle \beth _{0}=\aleph...