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# \aleph-preparacompact

Last-modified: 2010-12-19 (Æü) 19:32:42

## Name

• ℵ-preparacompact

## Definition

• A Hausdorff space X is called preparacompact if each open cover of X has an open refinement such that if is uncountable and if and for each with and for , then the set has a limit point iff the set has a limit point.

## Reference

• Davis, S.W. and Smith, J.C., The paracompactness of preparacompact spaces., Topology, Proc. Conf., Vol. 4, No.2, Ohio Univ. 1979, 345-360 (1980).