Abstract
We show that there exists an uncountably generated algebra every non-zero element of which is an everywhere surjective function on $\mathbb{C}$, that is, a function $f : \mathbb{C} \rightarrow \mathbb{C}$ such that, for every non void open set $U \subset \mathbb{C}$, $f(U) = \mathbb{C}$.
Citation
Richard M. Aron. José A. Conejero. Alfredo Peris. Juan B. Seoane-Sepúlveda. "Uncountably Generated Algebras of Everywhere Surjective Functions." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 571 - 575, august 2010. https://doi.org/10.36045/bbms/1284570738
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