A SEQUENTIAL PROPERTY OF C-P(X) AND A COVERING PROPERTY OF HUREWICZ

C-p(X) has the monotonic sequence selection property if there is for e ach f, and for every sequence (sigma(n) : n < omega) where for each n sigma(n), is a sequence converging pointwise monotonically to f, a seq uence (f(n) : n < omega) such that for each n f(n), is a term of sigma (n), and (f(n) : n < omega) converges pointwise to f. We prove a theor em which implies for metric spaces X that C-p(X) has the monotonic seq uence selection property if, and only if, X has a covering property of Hurewicz.