Talk:Uniform boundedness principle
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What the hell?! --JensMueller
The orginal non-Latex text of the proof
- For n = 1,2,3, ... let Xn = { x : ||T(x)|| ≤ n (∀ T ∈ F) } . By hypothesis, the union of all the Xn is X.
- Since X is a Baire space, one of the Xn has an interior point, giving some δ > 0 such that ||x|| < δ ⇒ x ∈ Xn.
- Hence for all T ∈ F, ||T|| < n/δ, so that n/δ is a uniform bound for the set F.
- I am reverting to the non-latex version, because the latex version adds nothing. (It has actually subtracted something: a rather important "implies" sign.) See Wikipedia:How_to_write_a_Wikipedia_article_on_Mathematics. Andrew Kepert 22:46, 14 Mar 2005 (UTC)