Algebrability of the set of everywhere surjective functions on C

被引：71

作者：

Aron, Richard M. ^{[1
]}

Seoane-Sepulveda, Juan B.

机构：

[1] Kent State Univ, Dept Math, Kent, OH 44242 USA

[2] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat, E-28040 Madrid, Spain

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2007年 / 14卷 / 01期

关键词：

lineability; spaceability; algebrability; everywhere surjective functions;

D O I：

10.36045/bbms/1172852242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：25 / 31

页数：7