The notion of base countable metacompact space is introduced through researching the relation between base countable metacompact space and its subspace. From the research
it draws the conclusion that base-normal countable metacompact space is base countable metacompact space
and it proves that open closed finite to 1 map preserves base countable metacompactness.
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references
John E.PORTER.Base-paracpmpact spaces[J].Topology and its Applications,2003,128:145-156.