Paracompactness and the Lindelöf property in countable products

Abstract In this paper, we prove the following: Let Y be a perfect paracompact (hereditarily Lindelof) space and {X n : n∈ω} be a countable collection of Cech-scattered paracompact (Lindelof) spaces, then the product Y ×∏ n ∈ ω X n is paracompact (Lindelof).