SEQUENTIAL CONVERGENCE IN Cp(X) AND A COVERING PROPERTY

Abstract

Let X be a perfectly1 normal Lindel¨of space. It is proved in Theorem 3 that the space has property S1(Γ,Γ) (as defined in [11]) if, and only if, it has property S1(Γ,Γ)∗ (as defined in [9]). This result is then used to answer Problem 8 of [9] negatively. Theorem 3 also supports a partial solution of Problem 5 of [9].