Uncountably Generated Algebras of Everywhere Surjective Functions
Aron, Richard M. ; Conejero, José A. ; Peris, Alfredo ; Seoane-Sepúlveda, Juan B.
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 571-575 / Harvested from Project Euclid
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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 $U \subset \mathbb{C}$, $f(U) = \mathbb{C}$.
Publié le : 2010-08-15
Classification:  Lineability,  spaceability,  algebrability,  everywhere surjective functions,  46E25,  15A03 
@article{1284570738,
     author = {Aron, Richard M. and Conejero, Jos\'e A. and Peris, Alfredo and Seoane-Sep\'ulveda, Juan B.},
     title = {Uncountably Generated Algebras of Everywhere Surjective Functions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 571-575},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1284570738}
}

Aron, Richard M.; Conejero, José A.; Peris, Alfredo; Seoane-Sepúlveda, Juan B. Uncountably Generated Algebras of Everywhere Surjective Functions. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  571-575. http://gdmltest.u-ga.fr/item/1284570738/