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
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
收藏
页码:25 / 31
页数:7
相关论文
共 3 条
  • [1] Lineability and spaceability of sets of functions on R
    Aron, R
    Gurariy, VI
    Seoane, JB
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (03) : 795 - 803
  • [2] Gelbaum B.R., 1964, Counterexamples in Analysis
  • [3] LEBESGUE H, 1904, LECONS INTEGRATION