View source for Talk:Quasi-uniform convergence

==Name of theorem==
There seems to be almost no support for the name "Arzelà–Aleksandrov theorem" as opposed to "[[Arzelà-Ascoli theorem]]" which is what it is called elsewhere in EOM.  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 20:08, 18 October 2017 (CEST)

:Really? I only know [https://en.wikipedia.org/wiki/Arzel%C3%A0%E2%80%93Ascoli_theorem this Arzelà-Ascoli theorem]. But maybe there are several Arzelà-Ascoli theorems? [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:36, 18 October 2017 (CEST)

:Even in [http://at.yorku.ca/cgi-bin/bbqa?forum=homework_help_2002&task=show_msg&msg=0247 this text] entitled "Arzela-Ascoli theoremS" I did not find anything like that... [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:48, 18 October 2017 (CEST)

:And still, [http://enc.biblioclub.ru/termin/1688665_ARCELA_-_ASKOLI_TEOREMA Russian version] says the same as our English version. Strange. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:53, 18 October 2017 (CEST)

:In [http://www.ams.org/journals/tran/1930-032-03/S0002-9947-1930-1501551-9/S0002-9947-1930-1501551-9.pdf GILLESPIE AND HURWITZ 1930], "Arzela condition" is mentioned on pages 528 and 538; otherwise Arzela is not mentioned. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 23:06, 18 October 2017 (CEST)

:In [http://www.dwc.knaw.nl/DL/publications/PU00012013.pdf Wolff 1919] it is called Arzela's theorem. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 23:27, 18 October 2017 (CEST)

:"In 1883 Arzelà (1983/1984) [2] gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued continuous functions on a compact interval to be continuous. Arzelà's work paved the way for several outstanding papers. A milestone was the P.S. Alexandroff convergence introduced in 1948 to tackle the question for a sequence of continuous functions from a topological space (not necessarily compact) to a metric space. In 2009, in the realm of metric spaces, Beer and Levi (2009) [10] found another necessary and sufficient condition through the novel notion of strong uniform convergence on finite sets. We offer a direct proof of the equivalence of Arzelà, Alexandroff and Beer–Levi conditions." [http://www.sciencedirect.com/science/article/pii/S0022247X10004531 Agata Casertaa, Giuseppe Di Maio, L˘ubica Holá 2010]. [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 23:32, 18 October 2017 (CEST)

::I think you're right: the definition of quasi-uniform continuity is due to Arzela, according to ''Scenes from the History of Real Functions'', F.A. Medvedev p.104 [https://books.google.co.uk/books?id=rqmABwAAQBAJ&pg=PA104].  The statement of the article [[Arzelà-Ascoli theorem]] needs correction.  [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 19:12, 19 October 2017 (CEST)