Paracompactness and the Lindelöf property in countable products

Screenableness in countable products

“…As a generalization of C-scattered spaces,Čech-scattered spaces introduced by Hohti and Ziqiu [8] play the same fundamental role in the study of paracompactness of countable products. In 2005, Aoki and Tanaka [1] extended the Hohti and Ziqiu's results by proving that if Y is a perfect paracompact space, and {X n : n ∈ ω} is a countable collection ofČech-scattered paracompact spaces, then the product Y × ∏ n∈ω X n is paracompact.…”

“…Remark 3.6. If {X n : n ∈ ω} is a countable collection ofČech-scattered screenable spaces, we can assume that X n =X for each n ∈ ω, and X is topped with Top(X)={a} for some a ∈ X, see [1,8]. Therefore, by Theorem 3.4, the product ∏ n∈ω X n is screenable.…”