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Ostrand  gave the following characterization of the covering dimension for metric spaces. A metric space X is of dimension ^w if and only if for each open cover CoiX and each integer k^n + 1 there exist k discrete families of open sets U\, U2, • • • ,Uk such that the union of any n + 1 of the Ui is a cover of X which refines C. The purpose of this paper is to generalize Ostrand's theorem to collectionwise normal spaces by using an argument similar to that of Michael [l, Theorem 2].doi:10.1090/s0002-9939-1970-0261533-5 fatcat:bsxcjvonsjhfbopkyymb3azlya