Algebrability of the set of everywhere surjective functions on $\mathbb{C}$
Aron, Richard M. ; Seoane-Sepúlveda, Juan B.
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 25-31 / Harvested from Project Euclid
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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.
Publié le : 2007-03-14
Classification:  lineability,  spaceability,  algebrability,  everywhere surjective functions,  46E25,  15A03 
@article{1172852242,
     author = {Aron, Richard M. and Seoane-Sep\'ulveda, Juan B.},
     title = {Algebrability of the set of everywhere surjective functions on $\mathbb{C}$},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 25-31},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1172852242}
}

Aron, Richard M.; Seoane-Sepúlveda, Juan B. Algebrability of the set of everywhere surjective functions on $\mathbb{C}$. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  25-31. http://gdmltest.u-ga.fr/item/1172852242/