Strong algebrability and residuality on certain sets of analytic functions

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.