Classification of selectors for sequences of dense sets of Cp(X)

For example, a space X satisfies S1(D,S) (resp., Sfin(D,S)) if whenever {Dn:n∈N} is a sequence of dense subsets of X, one can take points xn∈Dn (resp., finite Fn⊂Dn) such that {xn:n∈N} (resp., ⋃{Fn:n∈N}) is sequentially dense in X. Other properties are defined similarly. S1(D,D) (=R-separability) and Sfin(D,D) (=M-separability) for Cp(X) were already investigated by several authors. In this paper, we have gave characterizations for Cp(X) to satisfy other 6 properties above.