A topological space X is countably paracompact if and only if X satisfies the condition (A): For any decreasing sequence {Fi} of non-empty closed sets with ⋂i=1∞Fi=∅\documentclass[12pt]{minimal}
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\begin{document}$${\bigcap_{i=1}^{\infty} F_{i} = \emptyset}$$\end{document} there exists a sequence {Gi} of open sets such that ⋂i=1∞Gi¯=∅\documentclass[12pt]{minimal}
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\begin{document}$${\bigcap_{i=1}^{\infty}\overline{G_{i}}=\emptyset}$$\end{document} and Fi⊂Gi\documentclass[12pt]{minimal}
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\begin{document}$${F_{i} \subset G_{i}}$$\end{document} for every i. We will show, by an example, that this is not true in generalized topological spaces. In fact there is a μ\documentclass[12pt]{minimal}
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\begin{document}$${\mu}$$\end{document}-normal generalized topological space satisfying the analogue of A which is not even countably μ\documentclass[12pt]{minimal}
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\begin{document}$${\mu}$$\end{document}-metacompact. Then we study the relationships between countably μ\documentclass[12pt]{minimal}
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\begin{document}$${\mu}$$\end{document}-paracompactness, countably μ\documentclass[12pt]{minimal}
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\begin{document}$${\mu}$$\end{document}-metacompactness and the condition corresponding to condition A in generalized topological spaces.
