The theory of Cohen elements

Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras

“…The proofs we outlined here are clearly much simpler than the original proofs by the author [19], [21], and also significantly simpler than the improvements of these proofs given in [23], [54], [55].…”

“…Here we define % to be the relation ai % 02 if and only if o^i e 02 ^ on n. Since Q is a divisible group, a modification of the proof of lemma 4-9 gives again a map ^ : T^ -^ 0 such that ^ (di +^2) = ^ (di).^ (^2) (di, ^2 C T^) (and such that ^ (d) T^i (d) for every d e T^). By using standard factorization methods [48] it is also possible to arrange, a G % being given, that a C ^ (d).% for every d G T^ (in fact, the construction of the map y?i is sufficient to perform the embedding: C^ -^ T^ as in [18], and so the construction of [19] and [54] can be replaced by a few lines to obtain a quick solution of Kaplansky's problem, assuming the continuum hypothesis).…”

Propriétés multiplicatives universelles de certains quotients d'algèbres de Fréchet

“…, [9], [10], [17], [18]) de sa construction d'homomorphismes discontinus de C(K) (voir l'article [13] Pour n > 1 soit 03C3(n) ~ 0 l'entier défini par les relations q~(~) n q~.~n~+1. (0 rrtk p~ , h n -f-1 , n > 1).…”