Publication: Algebrability of the set of everywhere surjective functions on C
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2007
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Belgian Mathematical Soc Triomphe
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Abstract
We show that the set L of complex-valued everywhere surjective functions on C is aJgebrable. Specifically, 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 is an element of N, n algebraically independent everywhere surjective functions, f(1), f(2),..., f(n), so that for every non-constant polynomial P is an element of C[z(1), z(2),...,z(n)], P(f(1), f(2),...f(n)) is also everywhere surjective.
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Dedicated to the memory of our great friend and colleague, Vladimir Gurariy.
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R. M. Aron, V. I. Gurariy, and J. B. Seoane. Lineability and spaceability of sets of functions on R. Proc. A.M.S.,133 (2005) 795-803.
B. Gelbaum, and J. Olmsted. Counterexamples in analysis.Holden-Day, (1964).
H. Lebesgue. Ležcons sur lintegration. Gauthier-Willars (1904).