On the Čech number of Cp(X)

We discuss the Čech numbers of the spaces Cp(X) and Cp(X,I) (where the Čech number of a space Z is the pseudocharacter of Z in βZ). We establish the relation between the Čech numbers of Cp(X) and of Cp(X,I), find some upper and lower bounds for the Čech number of Cp(X,I) in terms of the cardinal functions of X, and discuss the minimal possible infinite value that the Čech number of Cp(X,I) can have.