Talk:Stone–Weierstrass theorem

message: When we say something about "pure states"...
is the reader supposed to know what a pure state is???  — Preceding unsigned comment added by 189.61.2.44 (talk) 01:37, 1 November 2019 (UTC)
thread_title:  Domain question 

message: Students of different disciplines or sub-disciplines are often taught about the "Weierstrass theorem," which may refer to the extreme value theorem, Stone-Weierstrass, Bolzano-Weierstrass, or who knows what.  Currently Weierstrass theorem redirects here, to Stone-Weierstrass theorem.  I think we should have it redirect to a disambiguation page of sorts, perhaps a page called, "Mathematical objects bearing the name of Karl Weierstrass," which would include a list of theorems, as well as a short description of the theorem so students can figure out which one is relevant.  Does this sound like a good idea? I brought this up at Talk:Karl Weierstrass as well, so please feel free to discuss it there. Smmurphy(Talk) 21:22, 18 July 2007 (UTC)
thread_title:  Weierstrass theorem currently redirects here 

message: The "See also" section has the following comment:
:However, as is shown in Rudin's Principles of Mathematical Analysis, one can easily find a polynomial P uniformly approximating ƒ by convolving ƒ with a polynomial kernel.
I find this remark a bit strange and naive.  Weierstrass' original proof is by convolving with a Gausian kernel.  Is it really reasonable to mention explicitely Rudin here?  I think not, and will change it, if nobody objects. --Bdmy (talk) 12:08, 3 April 2009 (UTC)
thread_title: About the comment in "See also"

message: Is the condition "Hausdorff" necessary? It seems that "compact" is enough. --Hang  —Preceding unsigned comment added by 219.236.149.32 (talk) 12:55, 28 April 2011 (UTC)
replies: text: I believe you are correct, the proof I know doesn't seem to use the Hausdorff assumption at all. AJ LaMotta (talk) 18:51, 29 May 2024 (UTC)
thread_title:  About the condition "Hausdorff" 

message: The article says:
:* f|S ∈ AS for every maximal set S ⊂ X such that AS contains no non-constant real functions.
So what is AS? --11:22, 30 March 2012 (UTC)
thread_title:  bishop theorem 

message: In this article we consider C(X) as super function spaces. But in this MSE question, L^2(X) is also considered when using Stone-Weierstrass theorem. Is it right? If yes, maybe we could replenish this. -- Namasikanam (talk) 03:15, 17 September 2019 (UTC)
thread_title:  Functions Domain: <math>L^2</math> functions? 

message: The link following the last but one reference points to the PDF of a paper by Hager
and is unrelated to the cited paper by Stone.
Bill
: Thanks for noticing. I removed the erroneous link. Saung Tadashi (talk) 17:02, 6 March 2021 (UTC)
thread_title:  "The Generalized Weierstrass Approximation Theorem" wrong PDF 

message: This new section refers to an English paper published in 1885 under the title On the possibility of giving an analytic representation to an arbitrary function of real variable. The related digital copy seems not to be available in the Internet Archive. Hence, it has been temporarily sourced by four academic papers, which, in my modest opinion, can be removed when the related primary source will be eventually made available on the web.Theologian81sp (talk) 21:51, 3 July 2021 (UTC)
thread_title:  Editorial history