In his [blog](http://recursed.blogspot.com.au/2013/09/by-usual-compactness-argument.html), Jeff Shallit asks, what was the first occurrence of the exact phrase, "by the usual compactness arguments," in the mathematical literature?


He reports that the earliest appearance he has found was in a paper from 1953: it's on page 400 of John W. Green, Pacific Journal of Mathematics 3 (2) 393-402. 


I found another example from that same year, on page 918 of F. A. Valentine, Minimal sets of visibility, Proc Amer Math Soc 4, 917-921. 


So, is this year the 60th anniversary of the first appearance of that phrase? 


If there was an earlier occurrence of the equivalent phrase in a language other than English, that, too, would be of interest. 



First occurrence of "by the usual compactness argument"?
There is a paper, written in German, called [Ueber Räume mit verschwindender erster Brouwerscher Zahl.](http://www.dwc.knaw.nl/DL/publications/PU00015637.pdf) by Urysohn and Alexandroff from 1928. (Notice that Urysohn drowned while swimming with Alexandroff in 1924)


The following quote is from page 810 (emphasis added):



> 
> Der Beweis dieser Tatsache ist wörtlich derselbe wie im Falle, wo $R$ der $R^n$ ist: es genügt zu zeigen, dass die erwähnte Trennungseigenschaft im Brouwerschen Sinne induktiv ist (**was aus der Kompaktheit von $R$ in der üblichen Weise folgt**), und dann den Phragmén-Brouwerschen Satz anzuwenden. 
> 
> 
> 


And here is my translation of that quote:



> 
> The proof of this fact is literally the same as in the case, where $R$ is $R^n$: it is sufficient to show that the mentioned separation property is inductive in the sense of Brouwer (**which follows from the compactness of $R$ in the usual fashion**), and then apply the [Phragmén-Brouwer Theorem](http://en.wikipedia.org/wiki/Phragmen%E2%80%93Brouwer_theorem).
> 
> 
> 


I suspect, that as soon as there was a good notion of compactness, people used it in a routine way as an standard argument.


