Answering a question on relative countable paracompactness (Q2703106)

This paper answers some questions of \textit{Y. Yasui} about relatively countably paracompact spaces. In particular, the author shows the following:NEWLINENEWLINENEWLINE(1) If a Tikhonov space \(Y\) is countably 1-paracompact in every Tikhonov space \(X\) that contains \(Y\) as a closed subspace then \(Y\) is linearly Lindelöf;NEWLINENEWLINENEWLINE(2) A Tikhonov countably compact space \(Y\) is countably 1-paracompact in every Tikhonov \(X\supset Y\) iff \(Y\) is compact;NEWLINENEWLINENEWLINE(3) If a Lindelöf space \(Y\) is a closed subspace of a regular space \(X\) then \(Y\) is countably 1-paracompact in \(X\).