Abstract
A topological space X is countably paracompact if and only if X satisfies the condition (A): For any decreasing sequence {F-i} of non-empty closed sets with boolean AND(infinity)(i=1) F-i = empty set there exists a sequence {G(i)} of open sets such that boolean AND(infinity)(i=1) (G) over bar (i) = empty set and F-i subset of G(i) for every i. We will show, by an example, that this is not true in generalized topological spaces. In fact there is a mu-normal generalized topological space satisfying the analogue of A which is not even countably mu-metacompact. Then we study the relationships between countably mu-paracompactness, countably mu-metacompactness and the condition corresponding to condition A in generalized topological spaces.