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It is shown that if a product of nonempty spaces is a &-space then for each infinite cardinal n some product of all but n of the factors has each n-fold subproduct n-X0-compact (each n-fold open cover has a finite subcover). An example is given, for each regular n, of a space X which is not n-N0-compact (so Xn+ is not a A:-space) for which Xn is a A:-space.doi:10.1090/s0002-9939-1972-0287503-0 fatcat:wakojb5xq5eapimy4calsdatqa