Abstract
We show that if there is no family of cardinality less than c which dominates ω ω ^\omega \omega , then the box product of countably many compact first-countable spaces is paracompact; hence the countable box product of compact metrizable spaces is paracompact if 2 ω = ω 2 {2^\omega } = {\omega _2} . We also give classes of forcing extensions in which many box products are paracompact.
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