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Algebrability of the set of everywhere surjective functions on C

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Aron, Richard M. and Seoane-Sepúlveda, Juan B. (2007) Algebrability of the set of everywhere surjective functions on C. Bulletin of the Belgian Mathematical Society-Simon Stevin, 14 (1). pp. 25-31. ISSN 1370-1444

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Official URL: http://projecteuclid.org/euclid.bbms/1172852242


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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.

Uncontrolled Keywords:Lineability; Spaceability; Algebrability; Everywhere surjective functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20081
Deposited On:22 Feb 2013 14:29
Last Modified:25 Nov 2016 12:26

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