Let X be a subspace of the product of nitely many ordinals. X
is countably metacompact, and X is metacompact i X has no closed subset
homeomorphic to a stationary subset of a regular uncountable cardinal. A
theorem generalizing these two results is: X is -metacompact i X has no
closed subset homeomorphic to a ( 1; : : : ; n)-stationary set where 1 < .
This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9939-01-06026-9. First published in Proc. Amer. Math. Soc. in 2001, published by the American Mathematical Society.
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