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We define, in a slightly unusual way, the rank of a partially ordered set. Then we prove that if X is a topological space and 
satisfies condition (F) and, for every x∈X, 
is of the form 
, where 
is Noetherian of finite rank, and every other 
is a chain (with respect to inclusion) of neighbourhoods of x, then X is metacompact. We also obtain a cardinal extension of the above. In addition, we give a new proof of the theorem ‘if the space X has a base 
of point-finite rank, then X is metacompact’, which was proved by Gruenhage and Nyikos.
