Re: [HM] Who invented the idea of an open set?
William C Waterhouse (wcw@math.psu.edu)
Fri, 17 Sep 1999 15:18:23 -0400 (EDT)
Yesterday (Thu, 16 Sep 1999), Bill Everdell <Everdell@aol.com> wrote:
> In a message dated 9/15/99, Udai Venedem writes:
>
> >... in his *De la puissance des ensembles parfaits de
> >points* (Acta Mathematica IV, 4 mars 1884, p.388), ...
> > [Cantor] announces:
> >*dans une prochaine communication, je montrerai (...) pour les
> >ensembles de points "non ferme/s"* ...
> ><<This "prochaine communication" never appeared in the Acta.
> >Does anyone know where else, if ever? >>
>
> Well, 1884 was not a good year for Cantor to have pursued such an otherwise
> promising byway. Here's a chronology of 1884 events following the
> publication of the paper in March that suggests Cantor may never even have
> *completed* such a paper:
>
> May, Cantor's first nervous breakdown. Brief hospitalization
> Aug, Cantor to Mittag-Leffler claiming he has proved the Continuum
> Hypothesis.
> ____ Cantor, "Ueber unendliche, lineare, Punktmannigfaltigkeiten VI" in Math.
> Ann. 23
> Nov, Cantor to Mittag-Leffler withdrawing claim he has proved the Continuum
> Hypothesis and claiming to have proved that the Hypothesis is false. In
> another letter the next day, he withdraws this new proof, too.
The (...) in the statement quoted is in fact precisely the
continuum hypothesis (which Cantor proved for closed sets
in that paper).
William C. Waterhouse
Penn State