you may recall that we now are quite sure, by Gregory Moore's precise
citations, that the concept of open set only emerged with Lebesgue's
1905, and Gregory Moore gave another good indication, as to distinguish
those who referred to "open sets" as "not closed", and those (Lebesgue)
as "complement of closed".
The question still "open" was to know if Cantor would ever have initiated
the concept. And indeed, in his *De la puissance des ensembles parfaits
de points* (Acta Mathematica IV, 4 mars 1884, p.388), he introduces (in
French) the concept and the wording of "ensemble ferm/e" (closed set).
But what is really interesting is that he announces:
*dans une prochaine communication, je montrerai (...) pour les ensembles
de points "non ferme/s"* (where "." is here for italic), or
*in a next paper soon to come, I will show (...) for "not closed" sets of
points*.
This "prochaine communication" never appeared in the Acta. Does anyone know
where else, if ever?
Udai Venedem
venedem@wanadoo.fr
http://perso.wanadoo.fr/alta.mathematica/