The Rothberger property on Cp(X, 2)

In this paper we analyze the Rothberger property on C-p(X, 2). A space X is said to have the Rothberger property (or simply X is Rothberger) if for every sequence < U-n : n is an element of omega > of open covers of X, there exists U-n is an element of U-n for each n is an element of omega co such that X = boolean OR U-n is an element of omega(n). We show the following: (1) if C-p(X, 2) is Rothberger, then X is pseudocompact; (2) for every pseudocompact Sokolov space X with t* (X) <= omega, C-p(X, 2) is Rothberger; and (3) assuming CH (the continuum hypothesis) there is a maximal almost disjoint family A for which the space C-p (Psi(A), 2) is Rothberger. Moreover, we characterize the Rothberger property on C-p(L, 2) when L is a GO-space. (C) 2015 Elsevier B.V. All rights reserved.