Open Access
august 2010 Uncountably Generated Algebras of Everywhere Surjective Functions
Richard M. Aron, José A. Conejero, Alfredo Peris, Juan B. Seoane-Sepúlveda
Bull. Belg. Math. Soc. Simon Stevin 17(3): 571-575 (august 2010). DOI: 10.36045/bbms/1284570738


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 $U \subset \mathbb{C}$, $f(U) = \mathbb{C}$.


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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.


Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1207.46025
MathSciNet: MR2731374
Digital Object Identifier: 10.36045/bbms/1284570738

Primary: 46E25
Secondary: 15A03

Keywords: algebrability , everywhere surjective functions , lineability , spaceability

Rights: Copyright © 2010 The Belgian Mathematical Society

Vol.17 • No. 3 • august 2010
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