In the papers of Gerlits-Nagy [4] and McCoy [6] a study is made of properties of a space X which imply or are equivalent to other properties of the space C(X) (i.e. space of continuous real-valued functions on X with the topology of pointwise convergence). A family 2 of open subsets of X is an w-cover of X iff every finite subset of X is contained in an element of 9. A space X has the y-property iff for every w-cover 9 of X there exists a sequence (D,,: n < u)E~~ such thatÂ