The Lindelöf number of Cp(X)×Cp(X) for strongly zero-dimensional X

We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M , C p ( X, M ) is a continuous image of a closed subspace of C p ( X ). It follows in particular, that for strongly zero-dimensional spaces X , the Lindelöf number of C p ( X )× C p ( X ) coincides with the Lindelöf number of C p ( X ). We also prove that l ( C p ( X n ) κ ) ≤ l ( C p ( X ) κ ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κ compact subspaces.