SPACES ON WHICH EVERY POINTWISE CONVERGENT SERIES OF CONTINUOUS FUNCTIONS CONVERGES PSEUDO-NORMALLY

Abstract. A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉∞n=0 of continuous functions from X to R, if the series n=0 |fn | converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum. 1