Abstract
We show that the set of analytic functions from $\mathbb C^2$ into $\mathbb C^2$, which are not Lorch-analytic is spaceable and strongly $\mathfrak {c}$-algebrable, but is not residual in the space of entire functions from $\mathbb C^2$ into $\mathbb C^2$. We also show that the set of functions which belongs to the disk algebra but not a Dales-Davie algebra is strongly $\mathfrak {c}$-algebrable and is residual in the disk algebra.
Citation
M.L. Lourenço. D.M. Vieira. "Strong algebrability and residuality on certain sets of analytic functions." Rocky Mountain J. Math. 49 (6) 1961 - 1972, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1961
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