Open Access
March 2007 Algebrability of the set of everywhere surjective functions on $\mathbb{C}$
Richard M. Aron, Juan B. Seoane-Sepúlveda
Bull. Belg. Math. Soc. Simon Stevin 14(1): 25-31 (March 2007). DOI: 10.36045/bbms/1172852242


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.


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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.


Published: March 2007
First available in Project Euclid: 2 March 2007

zbMATH: 1130.46013
MathSciNet: MR2327324
Digital Object Identifier: 10.36045/bbms/1172852242

Primary: 46E25
Secondary: 15A03

Keywords: algebrability , everywhere surjective functions , lineability , spaceability

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 1 • March 2007
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