A topological space X is a \Sigma\Sigma*-space provided for every sequence (fn) of continuous functions from X to R, if the series \Sigman|fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelof \Sigma\Sigma*-space has Rothberger property. We also construct, under the continuum hypothesis, a \Sigma\Sigma*-subset of R of cardinality continuum.
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Last modified October 26, 2004.