# alaoglu造句

## 例句与造句

1. Its importance comes from the Banach Alaoglu theorem.
2. The Banach Alaoglu theorem depends on Tychonoff's theorem about infinite products of compact spaces.
3. Conversely, every bounded sequence in a Hilbert space admits weakly convergent subsequences ( Alaoglu's theorem ).
4. Alaoglu and ErdQs's conjecture remains open, although it has been checked up to at least 10 7.
5. Under the weak topology the bounded sets coincide with the relatively compact sets which leads to the important Bourbaki Alaoglu theorem.
6. It's difficult to find alaoglu in a sentence. 用alaoglu造句挺难的
7. The weak operator topology is useful for compactness arguments, because the unit ball is compact by the Banach-Alaoglu theorem.
8. The "'Bourbaki Alaoglu theorem "'is a generalization by Bourbaki to dual topologies on locally convex spaces.
9. Unknown to Alaoglu and ErdQs, about 30 pages of Ramanujan's 1915 paper " Highly Composite Numbers " were suppressed.
10. Consequently, for normed vector space ( and hence Banach spaces ) the Bourbaki Alaoglu theorem is equivalent to the Banach Alaoglu theorem.
11. Consequently, for normed vector space ( and hence Banach spaces ) the Bourbaki Alaoglu theorem is equivalent to the Banach Alaoglu theorem.
12. In their 1944 paper, Alaoglu and ErdQs conjectured that the ratio of two consecutive colossally abundant numbers was always a prime number.
13. Alaoglu and ErdQs noted that all superabundant numbers are highly abundant, and asked whether there are infinitely many highly abundant numbers that are not superabundant.
14. Since the Banach Alaoglu theorem is proven via Tychonoff's theorem, it relies on the ZFC axiomatic framework, in particular the axiom of choice.
15. By the Banach Alaoglu theorem and the reflexivity of " H ", the closed unit ball " B " is weakly compact.
16. It should be cautioned that despite appearances, the Banach Alaoglu theorem does " not " imply that the weak-* topology is locally compact.
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