Algebrability of some families of Darboux-like functions

We prove that the class of all almost continuous in the sense of Stallings functions possessing the Perfect Road Property and the class of all almost continuous functions without the Perfect Road Property contain a 2^c$2^{\mathfrak{c}}$-generated free algebras. We prove also that the family of all extendable functions contains a 2^c$2^{\mathfrak{c}}$-dimensional linear space.