Talk:Stone–Čech compactification

message: I wonder if there is a principal reason to call this compactification Stone--Čech and not Čech--Stone. If a mathematical phenomenon is discovered by two people at the same time, the custom is to use their names in the alphabetical order. For some reason, the authors of this compactification are often referred in the opposite order. Any chance this is just bias of the English-speaking world? I would guess that the English-speaking mathematicians probably didn't hear about Čech's result until much later, when they were already accustomed to attributing this to Stone. If this is the case, then I believe that Wikipedia should stand as an example and present the names in the correct order.  — Preceding unsigned comment added by 2A00:23C7:85B9:401:948D:585E:D448:EAAD (talk) 10:02, 9 November 2020 (UTC)
replies: text: I agree with the preceding comment. It hasn't been addressed for four years. Why is it so? 147.231.89.4 (talk) 07:20, 9 April 2024 (UTC)
thread_title:  Naming injustice? 

message: I used this compactification just the other day and was able to reduce the volume of all things I won by 1.5 to 3 times.  Thanks Wikipedia!  —Preceding unsigned comment added by 70.162.83.30 (talk) 02:18, 17 September 2007 (UTC)
thread_title: Awesome

message: A section is named: An application: the dual space of the space of bounded sequences of reals. But we are speaking about the dual space of l^\infty(\mathbb{N}), i.e., about integers, not reals, aren't we? --Kompik (talk) 15:21, 31 January 2008 (UTC)
replies: text: Feeling ashamed of this silly mistake. Of course we are talking about reals and \mathbb{N} stands for sequences. --Kompik (talk) 14:13, 7 February 2008 (UTC)
thread_title:  Is the title of the application appropriate? 

message: Obviously compactification is of inherent interest, but are there any wellknown theorems in e.g. analysis, differential equations, etc, that hinges on the existence of a compactification?
YohanN7 (talk) 21:46, 7 July 2010 (UTC)
thread_title:  Applications? 

message: Where does the beta-notation come from?
Thanks!! 131.130.16.86 (talk) 11:47, 24 January 2011 (UTC)
replies: text: I don't know, but in general, compactifications are denoted by lowercase Greek letters.—Emil J. 14:23, 25 January 2011 (UTC)
thread_title:  Notation 

message: In this revision  the information that The Stone–Čech compactification was first considered by Tychonoff and later by Stone and Čech. The same information is given at given at Russian wikipedia ru:Компактификация Стоуна — Чеха.
I was trying to find whether this is true. According the sources I was able to find seems that it is not true.
Quote from Allen Shields: Years ago. The Mathematical Intelligencer, Volume 9, Number 2, 61-63, 
: Stone-Čech Compactification. Čech's contribution is Čech [1937]. We quote from his introduction:.
::An important result was added by Tychonoff [1929], who proved that complete regularity is the necessary and sufficient condition for a topological space to be a subset of some bicompact Hausdorff space. As a matter of fact, Tychonoff proves more, viz. that, given a completely regular space S, there exists a bicompact Hausdorff space \beta(S) such that (i) S is dense in \beta(S), (ii) any bounded continuous real function defined in the domain S admits of a continuous extension to the domain \beta(S).
: If this were correct, it would seem that an injustice had occurred, and one should call this the Tychonoff compactification. ... Reading Tychonoff one does not find result (ii) above cited by Čech.
Also the nice diagram on p.27 of Russell C. Walker: The Stone-Čech compactification might be of interest in this connection. In fact, the only source supporting this claim, that I was able to find, is C. Wayne Patty: Foundations of topology By , p. 236:
: The compactification (given in the proof of Theorem 6.41) that was constructed by Tychonoff is name in honor of Eduard Čech (1893-1960) and M.H. Stone (1903-2008) who, in 1937, independently developed its properties by proving the results we state as Theorems 6.42, 6.47, and 6.48.
Does anyone know about other sources supporting Tychonoff's precedence? If the claim is false, does anybody know where the misconception came from? --Kompik (talk) 22:43, 17 November 2011 (UTC)
replies: text: The wording in the article has been changed to 'The Stone–Čech compactification occurs implicitly in a paper by Tychonoff' see this edit. This agrees with the above quote from Shields' paper. So I guess this issue is resolved. --Kompik (talk) 10:24, 4 May 2012 (UTC)
thread_title: Tychonoff before Stone and Čech?

message: Is there a reason, eluding me, for calling the unique map βf : βX → K a 'lift' of f : X → K ? Given the shape of the diagram, I would have rather said that βf extends f along the map X → βX. In the closing paragraph of that first section, it is properly termed the extension property of the functor β. 199.84.42.113 (talk) 20:31, 29 February 2012 (UTC)
replies: text: Well, if you rotate the diagram 90 degrees to the left, it looks like a lift.  Is there some precise notion of the word lift you have in mind, that βf fails to be? --Trovatore (talk) 21:54, 29 February 2012 (UTC)
thread_title:  Unique map is a lift?