Algebraic structures in the sets of surjective functions (Q276798)

This paper is a nice contribution to the area of research called algebrability. If \(\mathcal{L}\) is a commutative algebra, a set \(A\subset\mathcal{L}\) is \(\lambda\)-algebrable if \(A\cup\{0\}\) contains a \(\lambda\)-generated subalgebra \(B\) of \(\mathcal{L}\). Algebrability results can be investigated in quite different environments; in this paper the authors are interested in algebrability results associated to sets of surjective functions \(f:\mathbb{K}\rightarrow\mathbb{K}\). For instance, it is proved that the set of everywhere but not strongly everywhere surjective complex functions is strongly \(\mathfrak{c}\)-algebrable. They also show that its \(2^{\mathfrak{c}}\)-algebrability is consistent with the ZFC model. Among the different techniques used along the paper, the exponential-like function method plays an important role.