A topological space X is a \Sigma\Sigma^{*}-space
provided for every sequence (f_{n}) of continuous functions
from X to **R**, if the series \Sigma_{n}|f_{n}| 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.**