Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

Let $U$ be a connected domain of existence in a $(\mathcal {DFC})$-space and let $\mathcal {E}(U)$ be the set of holomorphic functions on $U$ whose domain of existence is $U$. We construct a $\mathfrak {c}$-dimensional subspace within $\mathcal {E}(U) \cup \{0\}$ and we give sufficient conditions for $\mathcal {E}(U)$ to be strongly algebrable. We also prove that $\mathcal {E}(U) \cup \{0\}$ contains a closed algebra $\mathcal {A}$ as well as a dense algebra $\mathcal {B}$, both containing an infinite algebraically independent set.