Characterizations of strongly paracompact spaces. (English) Zbl 1258.54007

Zhang, Xin

Discrete Dyn. Nat. Soc. 2012, Article ID 916765, 5 p. (2012).

Summary: Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover. It is proved that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement. Moreover, it is shown that a space is linearly \(D\) provided that every increasing open cover of the space has a point-countable open refinement.

MSC:

54D20

Noncompact covering properties (paracompact, Lindelöf, etc.)

Keywords:

star-countable refinement

References:

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