Abstract
We show that the set ${\mathcal L}$ of complex-valued everywhere surjective functions on $\mathbb{C}$ is algebrable. Specifically, ${\mathcal L}$ contains an infinitely generated algebra every non-zero element of which is everywhere surjective. We also give a technique to construct, for every $n \in \mathbb N$, $n$ algebraically independent everywhere surjective functions, $f_1, f_2, \dots, f_n$, so that for every non-constant polynomial $P \in \mathbb{C}[z_1, z_2, \dots, z_n]$, $P(f_1, f_2, \dots, f_n)$ is also everywhere surjective.
Citation
Richard M. Aron. Juan B. Seoane-Sepúlveda. "Algebrability of the set of everywhere surjective functions on $\mathbb{C}$." Bull. Belg. Math. Soc. Simon Stevin 14 (1) 25 - 31, March 2007. https://doi.org/10.36045/bbms/1172852242
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